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RD Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Solutions

Question - 11 : - The curved surface area of a cylinder is 1320 cm2 and its base had diameter 21 cm. Find the height and the volume of the cylinder. [Use π = 22/7]

Answer - 11 : - Curved surface area of a cylinder = 1320 cm2
Diameter of the base = 21 cm

Question - 12 : - The ratio between the radius of the base and theheight of a cylinder is 2 : 3. Find the total surface area of the cylinder, ifits volume is 1617 cm3.

Answer - 12 : - Ratio between radius and height of a cylinder = 2:3
Volume =1617 cm3
Let radius (r) = 2x
Then height (h) = 3x
∴ Volume = πr2h

Question - 13 : - A rectangular sheet of paper, 44 cm x 20 cm, is rolled along its length of form a cylinder. Find the volume of the cylinder so formed.

Answer - 13 : - Length of sheet = 44 cm
Breadth = 20 cm
By rolling along length, the height of cylinder (h) = 20cm
and circumference of the base = 44cm

Question - 14 : - The curved surface area of a cylindrical pillar is 264m2 and its volume is 924 m3. Find the diameter and the height of the pillar.

Answer - 14 : - Curved surface area of a pillar = 264 m2
and volume = 924 m3
Let r be the radius and It be height, then 2πrh = 264

Question - 15 : - Two circular cylinders of equal volumes have their heights in the ratio 1 : 2. Find the ratio of their radii.

Answer - 15 : - Volumes of two cylinders are equal Ratio in theirheight h1 :h2 = 1: 2

Question - 16 : - The height of a right circular cylinder is 10.5 m. Three times the sum of the areas of its two circular faces is twice the” area of the curved surface. Find the volume of the cylinder.

Answer - 16 : - Height of a right circular cylinder = 10.5 m
3 x sum of areas of two circular faces
= 2 x area of curved surface
Let r be that radius,

Question - 17 : - How many cubic metres of earth must be dugout to sink a well 21 m deep and 6 m diameter? Find the cost of plastering the inner surface of the well at ₹9.50 per m2.

Answer - 17 : - Diameter of a well = 6 m
∴ Radius (r) = 6/2 = 3 m
Depth (h) = 21 m
∴ Volume of earth dugout =πr2h

Question - 18 : - The trunk of a tree is cylindrical and its circumference is 176 cm. If the length of the trunk is 3 m. Find the volume of the timber that can be obtained from the trunk.

Answer - 18 : - Circumference of a cylindrical trunk of a tree = 176cm

Question - 19 : - A cylindrical container with diameter of base 56 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 32 cm x 22 cm x 14 cm. Find the rise in the level of the water when the solid is completely submerged.

Answer - 19 : - Diameter of cylindrical container = 56 cm
∴ Radius (r) = 56/2 = 28 cm
Dimensions of a rectangular solid are = 32 cm x 22 cm x 14 cm
∴ Volume of solid = lbh
= 32 x 22 x 14 = 9856 cm3
∴ Volume of water in thecontainer = 9856 cm3
Let h be the level of water, then
πr2h = 9856

Question - 20 : - A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal.

Answer - 20 : - Length of metallic tube = 25 cm
Inner diameter = 10.4 cm
∴ Radius (r) = 10.4/2 = 5.2 cm
Thickness of metal = 8 mm
∴ Outer radius (R) = 5.2 +0.8 = 6.0 cm
Volume of metal used = π(R2 – r2) x h

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