Question

Find the volume and surface area of a sphere of radius $ 14 $ cm.
A.Volume $ 34,212 $ and surface area $ 2364 $
B.Volume $ 32,112 $ and surface area $ 2564 $
C.Volume $ 11498 $ and surface area $ 2464 $
D.Volume $ 33,333 $ and surface area $ 2400 $

Answer 1

Hint: Here we will take the given data and place its value in the formula for volume and the surface area and simplify it for the required resultant value by using the basic multiplication and the division operators.

Complete step-by-step answer:
Given that: radius $ r = 14 $ cm
Volume of the sphere can be given by –
\[V = \dfrac{4}{3}\pi {r^3}\]
Place the value of radius in the above equation and value of $ \pi = \dfrac{{22}}{7} $
\[V = \dfrac{4}{3}\left( {\dfrac{{22}}{7}} \right){(14)^3}\]
Split the power of cube, cube is the expression when the same number is multiplied thrice.
\[V = \dfrac{4}{3}\left( {\dfrac{{22}}{7}} \right)(14 \times 14 \times 14)\]
Common factors from the numerator and the denominator cancel each other.
\[V = \dfrac{4}{3}\left( {22} \right)(2 \times 14 \times 14)\]
Simplify the above expression –
 $ V = \dfrac{{34496}}{3} $
Find division of the term –
 $ V = 11498.66c{m^3} $ …. (A)
Now, Surface area of the sphere can be given by –
 $ SA = 4\pi {r^2} $
Place the given value in the above equation -
 $ SA = 4\left( {\dfrac{{22}}{7}} \right){(14)^2} $
Simplify the above expression –
 $ SA = 4\left( {\dfrac{{22}}{7}} \right)(14 \times 14) $
Simplify the above expression finding the multiplication and the division of the terms –
 $ SA = 2464c{m^2} $
From the given multiple choices – the option C is the correct answer.
So, the correct answer is “Option C”.

Note: Do not get confused between the volume and the area formula and place the specific units after it. Always remember that the volume is always measured in cubic units and the area is measured in square units.