A day full of math games & activities. Find one near you.

A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone. Is the given statement true or false and justify your answer.

Solution:

Given, a cylinder and a right circular cone are having the same base and same height

The volume of the cylinder is three times the volume of the cone

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

Volume of cone = 1/3 πr²h

Where, r is the radius of cone

h is the height of the cone

Volume of cylinder = πr²h

Where, r is the radius of cylinder

h is the height of the cylinder

Given, radius and height of cylinder and cone are equal

Volume of cylinder = 3(volume of cone)

Therefore, the given statement is true.

✦ Try This: The circumference of the base of a cylinder is 12 m and its height is 77 m. The volume of the cylinder is

Given, the circumference of the base of a cylinder is 12 m

Height, h = 77 m

We have to find the volume of the cylinder

Circumference of the base = 2πr

2πr = 12

πr = 6

r = 6/π m

Volume of cylinder = πr²h

Where, r is the radius of cylinder

h is the height of the cylinder

So, volume = π(6/π)²(77)

= 36(77)/π

Taking π = 3.14

Volume = 36(77) / (22/7)

= 36(77)(7) / 22

= 36(7)(7) / 2

= 18(49)

= 882 m³

Therefore, the volume of cylinder is 882 m³

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

NCERT Exemplar Class 9 Maths Exercise 13.2 Problem 6

A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone. Is the given statement true or false and justify your answer.

Summary:

The given statement “A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone” is true

☛ Related Questions: