Question

If the surface area of a sphere is \[144\pi \]\[c{m^2}\], then its radius is
A. 6cm
B. 8cm
C. 12cm
D. 10cm

Answer 1

Hint:Here we use the formula for surface area of a sphere and assuming the radius to be r we equate the value given in the question with the formula.

Formula used:Surface area of a sphere with radius r is \[4\pi {r^2}\].

Complete step-by-step answer:
Surface area of a sphere is the area that is covered by the surface of a three dimensional sphere. It is always measured in square units.
We are given a sphere whose surface area is \[144\pi \]\[c{m^2}\]
We know a sphere with radius r has surface area \[4\pi {r^2}\]
We equate the surface area of the sphere having radius r with the given value.
\[ \Rightarrow 4\pi {r^2} = 144\pi \]
Divide both the sides by \[4\pi \]
\[ \Rightarrow \dfrac{{4\pi {r^2}}}{{4\pi }} = \dfrac{{144\pi }}{{4\pi }}\]
Cancel the same terms from numerator and denominator.
\[ \Rightarrow {r^2} = 36\]
Take square root on both sides of the equation
\[ \Rightarrow \sqrt {{r^2}} = \sqrt {36} \]
We can write \[36 = {6^2}\]
\[ \Rightarrow \sqrt {{r^2}} = \sqrt {{6^2}} \]
Square root gets cancelled by square power
\[ \Rightarrow r = \pm 6\]
Since, r is the radius of the sphere. Therefore, we neglect the negative value of r.
\[\therefore r = 6\]cm

So, the correct answer is “Option A”.

Note:Students many times make the calculations complex by substituting in the value of \[\pi = 3.14\] in the formula and in the given value as well which gets complicated later to cancel out as the terms will be in decimal form. We can keep the value of \[\pi \] as it is because the answer of the surface area given has \[\pi \] in it, eventually it will cancel out. Always keep in mind we write the final answer along with the SI unit whichever is given in the question.