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The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r. Is the given statement true or false and justify your answer.

Solution:

Given, the volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals the volume of a hemisphere of radius r

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

Volume of cone = 1/3 πr²h

Where, r is the radius of the cone

h is the height of the cone

Given, volume of the cone fitted in a cube of edge 2r

So, h = 2r

Volume of cone = 1/3 πr²(2r)

= 2/3 πr³ cubic units

Volume of hemisphere = 2/3 πr³

Where, r is the radius of the hemisphere

Volume of cone with height 2r = volume of hemisphere

Therefore, the given statement is true.

✦ Try This: Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9cm.

Given, edge of cube = 9 cm

We have to find the volume of the largest right circular cone that can be cut out of a cube

Volume of cone = 1/3 πr²h

Where, r is the radius of the cone

h is the height of the cone

Here, r = 9/2 = 4.5 cm

h = 9 cm

So, volume = 1/3 π(4.5)²(9)

= 3π(4.5)²

= 190.85 cm³

Therefore, the volume of the largest cone is 190.85 cm³

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

NCERT Exemplar Class 9 Maths Exercise 13.2 Problem 5

The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r. Is the given statement true or false and justify your answer.

Summary:

The given statement “The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals the volume of a hemisphere of radius r” is true

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