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A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3. Is the given statement true or false and justify your answer.

Solution:

Given, a cone, a hemisphere and a cylinder stand on equal bases and have the same height

The ratio of their volumes is 1 : 2 : 3

We have to determine if the given statement is true or false.

Given, radius of cone = radius of hemisphere = radius of cylinder = r

Height of cone = height of hemisphere = height of cylinder = h

Volume of cone = 1/3 πr²h

Volume of hemisphere = 2/3 πr³

Volume of cylinder = πr²h

Ratio of volume = 1/3 πr²h : 2/3 πr³ : πr²h

= 1/3 : 2/3 : 1

= 1 : 2 : 3

Therefore, the given statement is true.

✦ Try This: The circumference of the base of a cylinder is 132 cm and its height is 25 cm. The volume of the cylinder is

Given, the circumference of the base of a cylinder is 132 cm

Height, h = 25 cm

We have to find the volume of cylinder

Circumference of the base = 2πr

2πr = 132

πr = 66

r = 66/π

Taking π = 22/7

r = 66 / (22/7)

r = 66(7) / 22

r = 3(7)

r = 21 cm

Volume of cylinder = πr²h

Where, r is the radius of cylinder

h is the height of the cylinder

So, volume = π(21)²(25)

= (22/7)(441)(25)

= 242550/7

= 34650 m³

Therefore, the volume of the cylinder is 34650 m³.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13

NCERT Exemplar Class 9 Maths Exercise 13.2 Problem 7

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3. Is the given statement true or false and justify your answer.

Summary:

The given statement “A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3” is true

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