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The Number of Solid Spheres, Each of Diameter 6 Cm that Can Be Made by Melting a Solid Metal Cylinder of Height 45 Cm and Diameter 4 Cm, is - Mathematics

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MCQ

The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:

Options

  • 3

  • 5

  • 4

  • 6

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Solution

Let r and h be the radius and the height of the cylinder, respectively.
Given:
Diameter of the cylinder = 4 cm
∴ Radius of the cylinder, r = 2 cm
Height of the cylinder, h = 45 cm
Volume of the solid cylinder = `pir^2h=pixx(2)^2xx45 cm^2=180pi cm^3`

Suppose the radius of each sphere be R cm.
Diameter of the sphere = 6 cm
∴ Radius of the sphere, R = 3 cm

Let n be the number of solids formed by melting the solid metallic cylinder.

n × Volume of the solid spheres = Volume of the solid cylinder

`=>nxx4/3 pi R^3=180pi`

`=>nxx4/3 pi(3)^3=180pi`

`=>n=(180xx3)/(4xx27)=5`

Thus, the number of solid spheres that can be formed is 5.

Hence, the correct option is B.

Concept: Surface Area of a Combination of Solids
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Q 44 | Page 91
RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Q 7 | Page 88
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