**Chapter 16 - Surface Area and Volume**

**Practice set 16.1**

**Practice set 16.1**

**1. Find the volume of a box if its length, breadth and height are 20 cm, 10.5 cm and 8 cm respectively. **

**Given:**

**Length of the box = 20 cm**

**Breadth of the box = 10.5 cm**

**Height of the box = 8 cm**

** **

**To find:**

**Volume of the box**

** **

**Solution:**

**Volume of the box = l × b × h**

**∴ Volume of the box = 20 × 10.5 × 8**

**∴ Volume of the box = 1680 cc**

** **

**Ans:** Volume of the box is 1680 cc

**2. A cuboid shape soap bar has volume 150 cc. Find its thickness if its length is 10 cm and breadth is 5 cm.**

**Given:**

**Volume of the soap bar = 150 cc**

**Length of the box = 10 cm**

**Breadth of the box = 5 cm**

** **

**To find:**

**Thickness or height of the soap bar**

** **

**Solution:**

**Volume of the box = l × b × h**

**∴ 150 = 10 × 5 × h**

**∴ \(\large \frac {150}{10\, ×\, 5}\) = h **

**∴ h = 3 cm**

** **

**Ans:** Thickness of the soap bar is 3 cm

**3. How many bricks of length 25 cm, breadth 15 cm and height 10 cm are required to build a wall of length 6 m, height 2.5 m and breadth 0.5 m?**

**Given:**

**Length of the brick = 25 cm**

**Breadth of the brick = 15 cm**

**Height of the brick = 10 cm**

**Length of the wall = 6 m = 6 × 100 cm = 600 cm**

**Breadth of the wall = 0.5 m = 0.5 × 100 cm = 50 cm**

**Height of the wall = 2.5 m = 2.5 × 100 cm = 250 cm**

** **

**To find:**

**Number of bricks required**

** **

**Solution:**

**Volume of the brick = l × b × h**

**∴ Volume of the brick = 25 × 15 × 10**

**∴ Volume of the brick = 3750 cc**

** **

**Volume of the wall = l × b × h**

**∴ Volume of the wall = 600 × 50 × 250**

**∴ Volume of the wall = 75,00,000 cc**

** **

**Number of bricks required = \(\large \frac {Volume \,of \, the \, wall}{Volume \,of \, the \, brick}\)**

**∴ Number of bricks required = \(\large \frac {75,00,000}{3750}\)**

**∴ Number of bricks required = 2000**

** **

**Ans:** 2000 bricks are required to build the wall.

**4. For rain water harvesting a tank of length 10 m, breadth 6 m and depth 3m is built. What is the capacity of the tank ? How many litres of water can it hold?**

**Given:**

**Length of the tank = 10 m = 10 × 100 cm = 1000 cm**

**Breadth of the tank = 6 m = 6 × 100 cm = 600 cm**

**Height of the tank = 3 m = 3 × 100 cm = 300 cm**

** **

**To find:**

**Capacity of the tank and litres of water the tank can hold**

** **

**Solution:**

**Capacity of tank = Volume of the tank**

**Volume of the tank = l × b × h**

**∴ Volume of the tank = 1000 × 600 × 300**

**∴ Volume of the tank = 18,00,00,000 cc**

** **

**∴ Capacity of tank = 18,00,00,000 cc**

** **

**And,**

**Litres of water the tank can hold = \(\large \frac {18,00,00,000\, cc}{1000}\) …[∵ 1000cc = 1 litre]**

**∴ Litres of water the tank can hold = 1,80,000 litres**

** **

**Ans:** The capacity of the tank is 18,00,00,000 cc and it can hold 1,80,000 litres of water.

**Practice set 17.2**

**Practice set 17.2****1. In each example given below, the radius of base of a cylinder and its height are given. Then find the curved surface area and total surface area. **

**(1) r = 7 cm, h = 10 cm **

**Given:**

**Radius of the cylinder = 7 cm**

**Height of the cylinder = 10 cm**

** **

**To find:**

**Curved surface area and Total surface area of the cylinder**

** **

**Solution:**

**Curved surface area of the cylinder = 2πrh**

**∴ Curved surface area of the cylinder = 2 × \(\large \frac {22}{7}\) × 7 × 10**

**∴ Curved surface area of the cylinder = 44 × 10**

**∴ Curved surface area of the cylinder = 440 sq.cm**

** **

**Total surface area of the cylinder = 2πr (h + r)**

**∴ Total surface area of the cylinder = 2 × \(\large \frac {22}{7}\) × 7 (10 + 7)**

**∴ Total surface area of the cylinder = 44 × 17**

**∴ Total surface area of the cylinder = 748 sq.cm**

** **

**Ans:** Curved surface area of the cylinder is 440 sq.cm and total surface area of the cylinder is 748 sq.cm.

**(2) r = 1.4 cm, h = 2.1 cm **

**Given:**

**Radius of the cylinder = 1.4 cm**

**Height of the cylinder = 2.1 cm**

** **

**To find:**

**Curved surface area and Total surface area of the cylinder**

** **

**Solution:**

**Curved surface area of the cylinder = 2πrh**

**∴ Curved surface area of the cylinder = 2 × \(\large \frac {22}{7}\) × 1.4 × 2.1**

**∴ Curved surface area of the cylinder = 44 × 0.2 × 2.1**

**∴ Curved surface area of the cylinder = 18.48 sq.cm**

** **

**Total surface area of the cylinder = 2πr (h + r)**

**∴ Total surface area of the cylinder = 2 × \(\large \frac {22}{7}\) × 1.4 (2.1 + 1.4)**

**∴ Total surface area of the cylinder = 44 × 0.2 × 3.5**

**∴ Total surface area of the cylinder = 44 × 0.7 **

**∴ Total surface area of the cylinder = 30.8 sq.cm**

** **

**Ans:** Curved surface area of the cylinder is 18.48 sq.cm and total surface area of the cylinder is 30.8 sq.cm.

**(3) r = 2.5 cm, h = 7 cm**

**Given:**

**Radius of the cylinder = 2.5 cm**

**Height of the cylinder = 7 cm**

** **

**To find:**

**Curved surface area and Total surface area of the cylinder**

** **

**Solution:**

**Curved surface area of the cylinder = 2πrh**

**∴ Curved surface area of the cylinder = 2 × \(\large \frac {22}{7}\) × 2.5 × 7**

**∴ Curved surface area of the cylinder = 44 × 2.5**

**∴ Curved surface area of the cylinder = 110 sq.cm**

** **

**Total surface area of the cylinder = 2πr (h + r)**

**∴ Total surface area of the cylinder = 2 × \(\large \frac {22}{7}\) × 2.5 (7 + 2.5)**

**∴ Total surface area of the cylinder = \(\large \frac {44}{7}\) × 2.5 × 9.5**

**∴ Total surface area of the cylinder = \(\large \frac {44\, ×\,23.75}{7}\) **

**∴ Total surface area of the cylinder = \(\large \frac {1045}{7}\) **

**∴ Total surface area of the cylinder = 149.28 sq.cm**

** **

**Ans:** Curved surface area of the cylinder is 110 sq.cm and total surface area of the cylinder is 149.28 sq.cm.

**(4) r = 70 cm, h = 1.4 cm **

**Given:**

**Radius of the cylinder = 70 cm**

**Height of the cylinder = 1.4 cm**

** **

**To find:**

**Curved surface area and Total surface area of the cylinder**

** **

**Solution:**

**Curved surface area of the cylinder = 2πrh**

**∴ Curved surface area of the cylinder = 2 × \(\large \frac {22}{7}\) × 70 × 1.4**

**∴ Curved surface area of the cylinder = 44 × 10 × 1.4**

**∴ Curved surface area of the cylinder = 44 × 14**

**∴ Curved surface area of the cylinder = 616 sq.cm**

** **

**Total surface area of the cylinder = 2πr(h + r)**

**∴ Total surface area of the cylinder = 2 × \(\large \frac {22}{7}\) × 70 (1.4 + 70)**

**∴ Total surface area of the cylinder = 44 × 10 × 71.4**

**∴ Total surface area of the cylinder = 440 × 71.4**

**∴ Total surface area of the cylinder = 31,416 sq.cm**

** **

**Ans:** Curved surface area of the cylinder is 616 sq.cm and total surface area of the cylinder is 31,416 sq.cm.

**(5) r = 4.2 cm, h = 14 cm**

**Given:**

**Radius of the cylinder = 4.2 cm**

**Height of the cylinder = 14 cm**

** **

**To find:**

**Curved surface area and Total surface area of the cylinder**

** **

**Solution:**

**Curved surface area of the cylinder = 2πrh**

**∴ Curved surface area of the cylinder = 2 × \(\large \frac {22}{7}\) × 4.2 × 14**

**∴ Curved surface area of the cylinder = 44 × 4.2 × 2**

**∴ Curved surface area of the cylinder = 369.6 sq.cm**

** **

**Total surface area of the cylinder = 2πr(h + r)**

**∴ Total surface area of the cylinder = 2 × \(\large \frac {22}{7}\) × 4.2 (14 + 4.2)**

**∴ Total surface area of the cylinder = 44 × 0.6 × 18.2**

**∴ Total surface area of the cylinder = 480.48 sq.cm**

** **

**Ans:** Curved surface area of the cylinder is 369.6 sq.cm and total surface area of the cylinder is 480.48 sq.cm.

**2. Find the total surface area of a closed cylindrical drum if its diameter is 50 cm and height is 45 cm. (π = 3.14)**

**Given:**

**Diameter of the cylindrical drum = 50 cm**

**Height of the cylindrical drum = 45 cm**

**π = 3.14**

** **

**To find:**

**Total surface area of the closed cylindrical drum**

** **

**Solution:**

**Radius of the cylindrical drum = \(\large \frac {Diameter\,of\,the\,cylindrical\,drum}{2}\)**

**∴ Radius of the cylindrical drum = \(\large \frac {50}{2}\)**

**∴ Radius of the cylindrical drum = 25 cm**

** **

**Total surface area of the cylindrical drum = 2πr (h + r)**

**∴ Total surface area of the cylindrical drum = 2 × 3.14 × 25 (45 + 25)**

**∴ Total surface area of the cylindrical drum = 6.28 × 25 × 70**

**∴ Total surface area of the cylindrical drum = 6.28 × 1750**

**∴ Total surface area of the cylindrical drum = 10,990 sq.cm**

** **

**Ans:** Total surface area of the cylindrical drum is 10,990 sq.cm

**3. Find the area of base and radius of a cylinder if its curved surface area is 660 sq.cm and height is 21 cm.**

**Given:**

**Curved surface area of the cylinder = 660 sq.cm**

**Height of the cylinder = 21 cm**

** **

**To find:**

**Area of base of the cylinder **

**Radius of the cylinder **

** **

**Solution:**

**Curved surface area of the cylinder = 2πrh**

**∴ 660 = 2 × \(\large \frac {22}{7}\) × r × 21**

**∴ 660 = 44 × r × 3**

**∴ \(\large \frac {660}{44\, ×\,3}\) = r**

**∴ r = 5 cm**

** **

**Area of base of the cylinder is a circle**

**∴ Area of base of the cylinder = πr²**

**∴ Area of base of the cylinder = 3.14 × (5)²**

**∴ Area of base of the cylinder = 3.14 × 25**

**∴ Area of base of the cylinder = 78.75 sq.cm**

** **

**Ans:** Area of base of the cylinder is 78.75 sq.cm and radius of the cylinder is 5 cm.

**4. Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is 28 cm and height is 20 cm. Find the approximate area of the sheet required to make a lid of height 2 cm for this container.**

**Given:**

**Diameter of the cylindrical container = 28 cm**

**Height of the cylindrical container = 20 cm**

**Height of the lid for the container = 2 cm**

** **

**To find:**

**Area of sheet required to make the cylindrical container**

**Area of sheet required to make a lid for the cylindrical container**

** **

**Solution:**

**Diameter of the cylindrical container = 28 cm**

**∴ Radius of the cylindrical container = \(\large \frac {28}{2}\)**

**∴ Radius of the cylindrical container = 14 cm**

** **

**Area of the sheet required to make the cylindrical container = Curved Surface area of the cylinder + Area of base of the cylinder**

**∴ Area of the sheet required to make the cylindrical container = 2πrh + πr² **

**∴ Area of the sheet required to make the cylindrical container = \((\)2 × \(\large \frac {22}{7}\) × 14 × 20\()\) + \((\large \frac {22}{7}\) × 14 × 14 \()\)**

**∴ Area of the sheet required to make the cylindrical container = (44 × 2 × 20) + (22 × 2 × 14)**

**∴ Area of the sheet required to make the cylindrical container = 1760 + 616**

**∴ Area of the sheet required to make the cylindrical container = 2376 sq.cm**

** **

**Radius of the lid = Radius of the cylinder, as the lid has to fit the cylindrical container**

** **

**Area of the sheet required to make a lid for the cylindrical container = Curved Surface area of the lid + Area of base of the lid**

**∴ Area of the sheet required to make a lid for the cylindrical container = 2πrh + πr² **

**∴ Area of the sheet required to make a lid for the cylindrical container = \((\)2 × \(\large \frac {22}{7}\) × 14 × 2\()\) + \((\large \frac {22}{7}\) × 14 × 14 \()\)**

**∴ Area of the sheet required to make a lid for the cylindrical container = (44 × 2 × 2) + (22 × 2 × 14)**

**∴ Area of the sheet required to make a lid for the cylindrical container = 176 + 616**

**∴ Area of the sheet required to make a lid for the cylindrical container = 792 sq.cm**

** **

**Ans:** Area of the sheet required to make the cylindrical container is 2376 sq.cm and area of the sheet required to make a lid for the cylindrical container is 792 sq.cm

**Practice set 17.3**

**Practice set 17.3****1. Find the volume of the cylinder if height (h) and radius of the base (r) are as given below.**

**(1) r = 10.5 cm, h = 8 cm **

**Given:**

**r = 10.5 cm**

**h = 8 cm **

** **

**To find:**

**Volume of the cylinder**

** **

**Solution:**

**Volume of the cylinder = πr²h**

**∴ Volume of the cylinder = \(\large \frac {22}{7}\) × (10.5)² × 8**

**∴ Volume of the cylinder = \(\large \frac {22}{7}\) × 10.5 × 10.5 × 8**

**∴ Volume of the cylinder = 22 × 1.5 × 84**

**∴ Volume of the cylinder = 2772 cu.cm**

** **

**Ans:** Volume of the cylinder is 2772 cu.cm

**(2) r = 2.5 m, h = 7 m **

**Given:**

**r = 2.5 cm**

**h = 7 cm **

** **

**To find:**

**Volume of the cylinder**

** **

**Solution:**

**Volume of the cylinder = πr²h**

**∴ Volume of the cylinder = \(\large \frac {22}{7}\) × (2.5)² × 7**

**∴ Volume of the cylinder = \(\large \frac {22}{7}\) × 2.5 × 2.5 × 7**

**∴ Volume of the cylinder = 22 × 6.25**

**∴ Volume of the cylinder = 137.5 cu.cm**

** **

**Ans:** Volume of the cylinder is 137.5 cu.cm

**(3) r = 4.2 cm, h = 5 cm **

**Given:**

**r = 4.2 cm**

**h = 5 cm **

** **

**To find:**

**Volume of the cylinder**

** **

**Solution:**

**Volume of the cylinder = πr²h**

**∴ Volume of the cylinder = \(\large \frac {22}{7}\) × (4.2)² × 5**

**∴ Volume of the cylinder = \(\large \frac {22}{7}\) × 4.2 × 4.2 × 5**

**∴ Volume of the cylinder = 22 × 0.6 × 21**

**∴ Volume of the cylinder = 277.2 cu.cm**

** **

**Ans:** Volume of the cylinder is 277.2 cu.cm

**(4) r = 5.6 cm, h = 5 cm **

**Given:**

**r = 5.6 cm**

**h = 5 cm **

** **

**To find:**

**Volume of the cylinder**

** **

**Solution:**

**Volume of the cylinder = πr²h**

**∴ Volume of the cylinder = \(\large \frac {22}{7}\) × (5.6)² × 5**

**∴ Volume of the cylinder = \(\large \frac {22}{7}\) × 5.6 × 5.6 × 5**

**∴ Volume of the cylinder = 22 × 0.8 × 28**

**∴ Volume of the cylinder = 492.8 cu.cm**

** **

**Ans:** Volume of the cylinder is 492.8 cu.cm

**2. How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?**

**Given:**

**Length of the rod = 90 cm **

**Diameter of the rod = 1.4 cm**

** **

**To find:**

**Amount of iron needed to make a rod**

** **

**Solution:**

**Rods are cylindrical in shape **

** **

**Radius of the rod = \(\large \frac {1.4}{2}\)**

**∴ Radius of the rod = 0.7 cm**

**And, Height of the rod = Length of the rod**

** **

**Amount of iron needed to make a rod = Volume of the rod**

**∴ Volume of the rod = πr²h**

**∴ Volume of the rod = \(\large \frac {22}{7}\) × (0.7)² × 90**

**∴ Volume of the rod = \(\large \frac {22}{7}\) × 0.7 × 0.7 × 90**

**∴ Volume of the rod = 22 × 0.1 × 63**

**∴ Volume of the rod = 138.6 cu.cm**

** **

**Ans:** Volume of the rod is 138.6 cu.cm

**3. How much water will a tank hold if the interior diameter of the tank is 1.6 m and its depth is 0.7 m ? **

**Given:**

**Internal diameter of the tank = 1.6 m**

**Depth of the tank = 0.7 m**

** **

**To find:**

**Volume of water the tank holds**

** **

**Solution:**

**Shape of the tank is cylindrical**

** **

**Internal radius of the tank = \(\large \frac {1.6}{2}\)**

**∴ Internal radius of the tank = 0.8 cm**

** **

**Height of the tank = Depth of the tank**

** **

**∴ Volume of water the tank holds = Internal volume of the tank**

**∴ Volume of water the tank holds = πr²h**

**∴ Volume of water the tank holds = \(\large \frac {22}{7}\) × (0.8)² × 0.7**

**∴ Volume of water the tank holds = 22 × 0.8 × 0.8 × 0.1**

**∴ Volume of water the tank holds = 22 × 0.064**

**∴ Volume of water the tank holds = 1.408 cu.cm**

** **

**Now,**

**1 cu.cm = 1000 l of water**

** **

**∴ Volume of water the tank holds = 1.408 × 1000**

**∴ Volume of water the tank holds = 1408 l**

** **

**Ans:** The tank holds 1408 l of water.

**4. Find the volume of the cylinder if the circumference of the cylinder is 132 cm and height is 25 cm.**

**Given:**

**Circumference of the cylinder = 132 cm**

**Height of the cylinder = 25 cm**

** **

**To find:**

**Volume of the cylinder**

** **

**Solution:**

**Circumference of the cylinder = 2πr**

**∴ 132 = 2 × \(\large \frac {22}{7}\) × r**

**∴ ∴ \(\large \frac {132\, ×\,7}{44}\) = r**

**∴ r = 3 × 7 **

**∴ r = 21 cm**

** **

**Volume of the cylinder = πr²h**

**∴ Volume of the cylinder = \(\large \frac {22}{7}\) × (21)² × 25**

**∴ Volume of the cylinder = \(\large \frac {22}{7}\) × 21 × 21 × 25**

**∴ Volume of the cylinder = 22 × 3 × 525**

**∴ Volume of the cylinder = 34650 cu.cm**

** **

**Ans:** Volume of the cylinder is 34650 cu.cm