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An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone (in cm³) is 1/6 πr³. Is the given statement true or false and justify your answer.

Solution:

Given, an edge of a cube measures r cm

If the largest possible right circular cone is cut out of this cube, then the volume of the cone is 1/6 πr³ cm³

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

Volume of the cone = 1/3 πr²h

Where, r is the radius of the cone

h is the height of the cone

Diameter of cone = r

Radius of cone, r = r/2

Height of cone, h = r

So, volume = 1/3 π(r/2)²r

= 1/3 π(r²/4)r

Volume = 1/12 πr³

Therefore, the given statement is false.

✦ Try This: An edge of a cube measures 2r cm. If the largest possible right circular cone is cut out of this cube, then find the volume of the cone (in cm³).

Given, an edge of a cube measures r cm

Largest possible right circular cone is cut out of this cube

We have to determine the volume of the cone

Volume of the cone = 1/3 πr²h

Where, r is the radius of the cone

h is the height of the cone

Diameter of cone = 2r

Radius of cone, r = r

Height of cone, h = 2r

So, volume = 1/3 π(r)²(2r)

= 2/3 πr²(r)

Therefore, Volume of the cone = 2/3 πr³

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

NCERT Exemplar Class 9 Maths Exercise 13.2 Sample Problem 2

An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone (in cm³) is 1/6 πr³. Is the given statement true or false and justify your answer.

Summary:

The given statement “An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone (in cm³) is 1/6 πr³” is false

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