Question

A solid right Circular Cone of
radius 2m and height 27 m is
melted and recasted into
asphere find the volume
and Surface area of sphere.​

Answer 1

$\sf\large\underline\blue{Given:}$

$\tt{\implies Radius\:_{(cone)}=2m}$

$\tt{\implies Height\:_{(cone)}=27m}$

$\sf\large\underline\blue{To\: Find:}$

$\tt{\implies Volume\:_{(sphere)}=?}$

$\tt{\implies Surface\: area\:_{(sphere)}=?}$

$\sf\large\underline\blue{Solution:}$

At first we have to calculate the the value of cone by applying formula. Then calculate the the volume of sphere and it's surface area:]

$\sf\large\underline\blue{Formula\: used:}$

$\tt{\implies Volume\:_{(sphere)}=\dfrac{4}{3}\pi\:r^3}$

$\tt{\implies Surface\: area\:_{(sphere)}=4\pi\:r^2}$

• Now calculate volume of cone:]

$\tt{\implies Volume\:_{(cone)}=\dfrac{1}{3}\pi\:r^2\:h}$

$\tt{\implies Volume\:_{(cone)}=\dfrac{1}{3}*\dfrac{22}{7}*2^2*27}$

$\tt{\implies Volume\:_{(cone)}=\dfrac{22*4*27}{3*7}}$

$\tt{\implies Volume\:_{(cone)}=\dfrac{2376}{21}m^3}$

=>Volume of cone=Volume of sphere:]

$\tt{\implies Volume\:_{(sphere)}=\dfrac{4}{3}\pi\:r^3}$

$\tt{\implies \dfrac{4}{3}*\dfrac{22}{7}r^3=\dfrac{2376}{21}}$

$\tt{\implies \dfrac{88r^3}{21}=\dfrac{2376}{21}}$

$\tt{\implies 88r^3=2376}$

$\tt{\implies r^3=27}$

$\tt{\implies r^3=3^3\implies r=3m}$

• Now calculate surface area here:]

$\tt{\implies Surface\: area\:_{(sphere)}=4*\dfrac{22}{7}*3^2}$

$\tt{\implies Surface\: area\:_{(sphere)}=\dfrac{4*22*9}{7}}$

$\tt{\implies Surface\: area\:_{(sphere)}=\dfrac{792}{7}m^2}$

• Now calculate volume of sphere:]

$\tt{\implies Volume\:_{(sphere)}=\dfrac{4}{3}\pi\:r^3}$

$\tt{\implies Volume\:_{(sphere)}=\dfrac{4}{3}*\dfrac{22}{7}*3^3}$

$\tt{\implies Volume\:_{(sphere)}=\dfrac{4*22*27}{3*7}}$

$\tt{\implies Volume\:_{(sphere)}=\dfrac{2376}{21}m^3}$

$\sf\large{Hence,}$

$\tt{\implies Volume\:_{(sphere)}=\dfrac{2376}{21}m^3}$

$\tt{\implies Surface\: area\:_{(sphere)}=\dfrac{792}{7}m^2}$

Answer 2

Answer:

volume of sphere is 113.04 cube m.

and

surface area of sphere is 113.04 sq.m