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Solid cones with a base radius of 1 mm and a height of 1 cm are formed by melting a solid metallic cylinder with a base radius of 3 cm and a height of 5 cm. Then there are ____ cones.

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Detailed Solution

Solid cones with a base radius of 1 mm and a height of 1 cm are formed by melting a solid metallic cylinder with a base radius of 3 cm and a height of 5 cm. Then there are 13500 cones.
It is given that a solid cone with a base radius of 1 mm and a height of 1 cm is formed by melting a solid metallic cylinder with a base radius of 3 cm and a height of 5 cm.
We know that the volume of the cylinder is

π r 2 h,

where r is the radius of the cylinder and h is its height.
The volume of the cone is

13 π R 2 h,

where R is the radius of the cone and h is its height.
We know that

1 mm = 110 cm

.
Height of the cone is 1 cm.
Therefore the number of cones can be calculated as,

n = Volume of the cylinder Volume of one cone ⇒ n = π 32 × 5 13 π 1102 × 1 ⇒ n = 9 × 5 13 × 1100 ⇒ n = 13500

Hence there are 13500 such cones.

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