Question

The surface area of a solid metallic sphere is 616 cm². It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use it =`22/7`)

Answer 1

Given height of cone (h) = 28 cm

Given surface area of Sphere = 616cm²

We know surface area of sphere = 4πr²

⇒ 4πr² = 616

⇒ `r^2=(616xx7)/(4xx22)`

⇒ r² = 49

⇒ r = 7cm

∴ Radius of sphere(r) = 7cm

Let r₁ be radius of cone

Given volume of cone = Volume of sphere

Volume of cone = `1/3pi(r^2)h`

`V_1=1/3pi(r_1)^2xx28cm^3`    ...........(1)

Volume of sphere `=(V_2)=4/3pir^3`

`V_2=4/3pi(7)^3cm^3`   .........(2)

(1) = (2) ⇒ V₁ = V₂

⇒ `1/3pi(r_1)^2xx28=4/3pi(7)^3`

⇒ `r_1^2 = 49`

r₁ = 7cm

Radius of cone (r₁) = 7cm

Diameter of base of cone (d₁) = 2x7 = 14cm