Question

a metalic sphere of radius 14 cm is melted and recast in small right circular cones each of diameter 7cm and height 8 cm find , how many such cones are formed ​

Answer 1

GIVEN

a metalic sphere of radius 14 cm is melted and recast in small right circular cones each of diameter 7cm and height 8 cm.

TO FIND

Find how many cones are formed

SOLUTION

• Radius of sphere = 14cm
• Volume of sphere = ?

Volume of sphere

→ 4/3πr³

→ 4/3 × 22/7 × 14 × 14 × 14

→ 4/3 × 22 × 2 × 14 × 14

→ 34496/3

→ 11498.6 cm³

Now,

• diameter of cone = 7cm
• Radius of cone = 7/2cm
• Height of cone = 8cm
• Volume of cone = ?

Volume of cone

→ 1/3πr³

→ 1/3 × 22/7 × 7/2 × 7/2 × 7/2

→ 1/3 × 11 × 1 × 7/2 × 7/2

→ 539/12

→ 44.91 cm³

Number of cones are formed

→ Volume of sphere/volume of cone

→ 11498.6/44.91

→ 256.03

Hence, the number of cones are formed i.e 256.03

Answer 2

Given:-

• Radius of sphere :- 14cm
• Diameter of cone :- 7cm
• Height :- 8cm

To find :-

• No. of cones formed

Solution:-

• Volume of sphere :- $\sf{ \dfrac{4}{3} \pi r^3}$

$\implies \sf{ \dfrac{4}{3} \times \dfrac{22}{7} \times 14 \times 14 \times 14}$

$\implies \sf{ \dfrac{4}{3} \times 22 \times 2 \times 14 \times 14}$

$\implies \sf{ \dfrac{ 34496}{3}}$

$\implies \sf{ 11498.6 cm^2}$

Now,

• Volume of cone :- $\sf{ \dfrac{1}{3} \pi r^3}$

$\implies \sf{ \dfrac{1}{3} \times 11 \times \dfrac{7}{2} \times \dfrac{7}{2}}$

$\implies \sf{ \dfrac{539}{12}}$

$\implies \sf{ 44.91 cm^3}$

No. of cone :- $\sf{ \dfrac{ Volume \; of \; sphere}{volume \; of \; cone}}$

$\implies \sf{ \dfrac{ 11498.6}{44.91}}$

$\implies \sf{ 256.03}$

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