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Solution for 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) - CBSE Class 10 - Mathematics

ConceptVolume of a Combination of Solids

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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RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 14: Surface Areas and Volumes
Q: 43
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.
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