Question

A solid piece of iron of dimensions 49 × 33 × 24 cm is moulded into a sphere. The radius of the sphere is
(a)21 cm
(b)28 cm
(c)35 cm
(d)none of these

Answer 1

Answer:

The radius of a sphere is 21 cm .

Among the given options option (a) 21 cm is the correct answer.

Step-by-step explanation:

Given :  

Volume of solid iron piece = 49 × 33 × 24 cm³

Let r be the radius of a sphere.

 

Volume of solid iron piece (cuboid) =  Volume of sphere

[solid iron piece is moulded into a sphere]

49 × 33 × 24 cm³ = 4/3 πr³

49 × 33 × 24 cm³ = 4/3 × 22/7 × r³

r³ = (49 × 33 × 24 × 3 × 7)/ (4 × 22)

r³ = 49 × 3 × 3 × 3 × 7

r³ = 7² × 3³ × 7¹

r³ = 7³ × 3³

r³ = 21³

r = 21 cm  

Radius of a sphere = 21 cm

Hence, the radius of a sphere is 21 cm

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Given,

Dimensions of solid piece of iron = 49 × 33 × 24 cm

Volume of Cuboid = Volume of Sphere

$lbh = \: \frac{4}{ 3} \pi {r}^{3} \\ \\ 49 \times 33 \times 24 = \frac{4}{3} \times \pi \times {r}^{3} \\ \\ 38808 = \frac{4}{3} \times \frac{22}{7} \times {r}^{3} \\ \\ 38808 = \frac{88}{21} \times {r}^{3} \\ \\ 38808 \times \frac{21}{88} = {r}^{3} \\ \\ 441 \times 21 = {r}^{3} \\ \\ {r}^{3} = 21 \times 21 \times 21 \\ \\ r = \sqrt[3]{21 \times 21 \times 21} \\ \\ r = 21cm$

Therefore, the radius of sphere is 21cm.