# 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

**☛ Related Questions:**

- The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter a . . . .
- If the radius of a right circular cone is halved and height is doubled, the volume will remain uncha . . . .
- In a right circular cone, height, radius and slant height do not always be sides of a right triangle . . . .

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