Question

2.
a) A cone of height 24cm and radius of base 6cm made up of modelling
clay. A child reshapes it in the form of a sphere. Find the radius of the
sphere and also find its T.S.A. ​

Answer 1

Step-by-step explanation:

first you find the volume of cone

then volume of cone is equal to volume of sphere 4/3 πr3

then you get radius r of sphere

then put r in 4 πrsqare you get total surface area

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Answer 2

Given:-

• Height of cone:- 24cm
• Radius of base :- 6cm

To find:-

• Radius of sphere
• T.S.A. of sphere

Solution:-

A child reshapes the cone in the form of a sphere. So,

Volume of cone = Volume of sphere

${\boxed{\sf{\blue{ \dfrac{1}{3} \pi r^2 h = \dfrac{4}{3} \pi r^3}}}}$

$\sf{ \dfrac{1}{ \cancel{3}} \times \cancel{ \pi} \times 6 \times 6 \times 24 = \dfrac{4}{ \cancel{3}} \times \cancel{ \pi} \times r^3}$

$\sf{6 \times 6 \times 24 = 4 \times r^3}$

$\sf{864 = 4 \times r^3}$

$\sf{ \cancel{ \dfrac{864}{4}} = r^3}$

$\sf{216 = r^3}$

$\sf{(6)^3 = r^3}$

${\boxed{\sf{\purple{\dag \; 6 = r}}}}$

★ Hence, radius of sphere is 6cm.

Now,

${\boxed{\sf{\red{T.S.A. of sphere = 4 \pi r^2}}}}$

$\implies \sf{4 \times \dfrac{22}{7} \times 6 \times 6}$

$\implies \sf{144 \times \dfrac{22}{7}}$

${\boxed{\sf{\pink{\dag \; T.S.A. \; of \; sphere = 452.16cm^2}}}}$

$\rule{200}{2}$