Question

answer the above question
chapter: Arithmetical Ability​

Answer 1

The required radius of sphere is 75 cm = 0.75 m

Answer 2

Answer- The above question is from the chapter 'Surface Areas and Volumes'.

Concepts used: 1) Melting a solid and then recasting it into another solid form equals both of the volumes of the solids.

Volume of cylinder = Volume of sphere

2) Volume of cylinder = πr²h

3) Volume of sphere = $\frac{4}{3} \pi r^{3}$

4) Diameter (d) = 2r

Given question: A metallic solid cylinder of height 1 m and base radius 0.75 m is melted and cast into a solid sphere. The diameter of the sphere (in m) so formed is _____ .

Solution: Volume of cylinder = Volume of sphere

πr²h = $\frac{4}{3} \pi R^{3}$

0.75 × 0.75 × 1 = $\frac{4}{3} \times R^{3}$

$\frac{75^{2} \: * \: 3}{4 \: * \: 10000}$ = R³

R³ = $\frac{16875}{40000}$

R³ = 0.421875‬

R = ∛0.421875‬

R = 0.75 m

d = 2R

d = 2 × 0.75

d = 1.5 m

∴ The diameter of the sphere (in m) so formed is 1.5 m .