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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 = 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
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