Question

Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Answer 1

Given, Weight of one solid sphere, m₁ = 5920 g

And weight of another solid sphere, m₂ = 740 g

Diameter of the smaller sphere = 5 cm

∴ Radius of the smaller sphere, r₂ = `5/2`, m₂ = 740 g

We know that, Density = `("Mass" (M))/("Volume" (D))`

⇒ Volume, `V = M/D`

⇒ `V_1 = 5920/D cm^3`   ...(i)

And `V_2 = 740/D cm^3`  ...(ii)

On dividing eqution (i) by equation (ii), we get

`V_1/V_2 = (5920/D)/(740/D)`

∵ Volume of a sphere = `4/3 pir^3`

`(4/3 pir_1^3)/(4/3 pir_2^3) = 5920/740`

⇒ `(r_1/r_2)^3 = 592/74`

⇒ `(r_1/(5/2))^3 = 592/74`   ...`[∵ r_2 = 5/2 cm]`

⇒ `r_1^3/(125/8) = 592/74`

⇒ `(8r_1^3)/125 = 592/74`

⇒ `r_1^3 = 592/74 xx 125/8`

= `74000/592`

= 125

∴ r₁ = 5 cm  ...[Taking positive value of the cube root]

Hence, the radius of larger sphere is 5 cm.