RD Sharma 2020 solution class 9 chapter 19 Surface Area and Volume of a Right Circular Cylinder VSAQS

VSAQS

Page-19.31

Question 1:

Write the number of surfaces of a right circular cylinder.

Answer 1:

Let us list out the surfaces of a right circular cylinder.

1. Lateral surface

2. Lower circular base

3. Upper circular covering

Therefore, a right circular cylinder has a total of 3 surfaces.

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:

Total Surface Area of a cylinder =

Curved Surface Area of a cylinder =

Ratio of Total Surface Area (TSA) to Curved Surface Area (CSA) is given by,

The ratio of Total Surface Area to Curved Surface Area is (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:

Given data is as follows

We have to find the total surface area of this cylinder

It is given that

Therefore

Therefore;

(As)

So;

Therefore;

Question 4:

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

Answer 4:

Let r₁ and r₂ be the radii of the two cylinders respectively and h₁ and h₂ are the heights of the two cylinders respectively. It is given that and

We are asked to find the ratio of the volumes of the two cylinders

Now;

Therefore the ratio of the volumes of the two cylinders is