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

Question - 1 : - Write the number of surface of a right circular cylinder.

Answer - 1 : - Three, two circular and one curved.

Question - 2 : - Write the ratio of total surface area to the curved surface area of a cylinder of radius r and height h.

Answer - 2 : -

∵ Radius = r
and height = h
∴ Curved surface area = 2πrh
and total surface area = 2πr(h + r)
∴ Ratio = 2πr(h + r) : 2πrh
= h + r : h

Question - 3 : - The ratio between the radius of the base and height of a cylinder is 2 : 3. If its volume is 1617 cm3, find the total surface area of the cylinder.

Answer - 3 : - Ratio in radius and height of the cylinder = 2 : 3
Let radius (r) = 2x
Then height (h) = 3x
∴ Volume = πr2h

Question - 4 : - If the radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3, then find the ratio of their volumes.

Answer - 4 : -

Ratio of radii of two cylinder = 2:3
Let radius of first cylinder (r1)= 2x
and second cylinder (r2) = 3x
and ratio in their heights = 5:3
Let height of first cylinder (h1) = 5y
and height of second (h2) = 3y
∴ Volumeof the first cylinder =πr2h
= π x (2x)2 x 5y = 20πx2y
and volume of second cylinder = π(3x)2 x 3y = 27πx2y
Now ratio between then,
= 20πx2y: 21πx2y
= 20 : 27

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