#### 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`)

#### Solution

Given height of cone (h) = 28 cm

Given surface area of Sphere = 616cm^{2}

We know surface area of sphere = 4πr^{2}

⇒ 4πr^{2} = 616

⇒ `r^2=(616xx7)/(4xx22)`

⇒ r^{2} = 49

⇒ r = 7cm

∴ Radius of sphere(r) = 7cm

Let r_{1} 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) ⇒ V_{1} = V_{2}

⇒ `1/3pi(r_1)^2xx28=4/3pi(7)^3`

⇒ `r_1^2 = 49`

r_{1} = 7cm

Radius of cone (r_{1}) = 7cm

Diameter of base of cone (d_{1}) = 2x7 = 14cm

Is there an error in this question or solution?

Solution 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`) Concept: Volume of a Combination of Solids.