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Which of the following statement(s) given below is / are TRUE? A: Height of a cone of volume equal to the volume of a cylinder of base radius similar to that of the cone is 3 times that of the cylinder. B: A prism of the square base of the side 4 cm is divided into 8 equal pieces by cutting the horizontal planes. If the height of the prism is 32 cm, the volume of each small piece is 64 cm3. C: The ratio of the numerical value of the volume of a sphere with radius R to its surface area is R : 3.

Which of the following statement(s) given below is / are TRUE? A: Height of a cone of volume equal to the volume of a cylinder of base radius similar to that of the cone is 3 times that of the cylinder. B: A prism of the square base of the side 4 cm is divided into 8 equal pieces by cutting the horizontal planes. If the height of the prism is 32 cm, the volume of each small piece is 64 cm3. C: The ratio of the numerical value of the volume of a sphere with radius R to its surface area is R : 3. Correct Answer All

GIVEN:

Three statements.

CONCEPT:

Mensuration

FORMULA USED:

Volume of cone = (πR2h) / 3

The volume of cylinder = πR2H

The volume of cube = S3

Volume of sphere = 4πR2 / 3

The surface area of sphere = 4πR

CALCULATION:

A:

Let the height of the cone is h and the height of the cylinder is H.

Now,

(πR2h) / 3 = πR2H

⇒ h = 3H

B:

A prism of the square base is a cuboid.

Height of cuboid = 32 cm

Height of each small equal pieces = 32/8 = 4 cm

Hence, each small equal piece is a cube.

The volume of each cube = 43

= 64 cm3

C:

The volume of sphere = 4πR3/3

The surface area of sphere = 4πR2

Now,

= (4πR3/3) : 4πR2

= R : 3

Hence, all statements A, B, and C are TRUE. 

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