Question

Find the radius of a sphere whose surface area is \[154\;c{m^2}\] .

Answer 1

Hint: Sphere is a three dimensional figure. Let \[r\] be the radius of the sphere. We know that the surface area of the sphere is \[ = 4\pi {r^2}\] . Surface area of the sphere is given. Substituting in the formula we get the value of \[r\] . Since they did not give the value of \[\pi \] , we take \[\pi = \dfrac{{22}}{7}\] . We note that the area is in square centimetres. So the unit of the radius will be in centimetre only.

Complete step-by-step answer:
Careful about the area that is given, that is curved surface area or total surface area. Both have different formulas for area.
 Total surface area of the sphere is \[ = 154\;c{m^2}\] .
Also, the surface area of the sphere is \[ = 4\pi {r^2}\] . Where, \[r\] is the radius of the sphere.
 \[ \Rightarrow 4\pi {r^2} = 154\]
Substituting the value of \[\pi = \dfrac{{22}}{7}\] . We get,
 \[ \Rightarrow 4 \times \dfrac{{22}}{7} \times {r^2} = 154\]
Divide by 7 on both sides, we get:
 \[ \Rightarrow 4 \times 22 \times {r^2} = 154 \times 7\]
Rearranging the equation for \[{r^2}\] .
 \[ \Rightarrow {r^2} = \dfrac{{154 \times 7}}{{22 \times 4}}\] (Simple multiplication)
 \[ \Rightarrow {r^2} = \dfrac{{1078}}{{88}}\]
 \[ \Rightarrow {r^2} = 12.25\]
Taking square root on both side we get,
 \[ \Rightarrow r = \sqrt {12.25} \]
 \[ \Rightarrow r = 3.5\]
Thus, the radius of the sphere is \[3.5\;cm\]
So, the correct answer is “3.5 cm”.

Note: Surface area is the total area on the surface of a three-dimensional figure. If you know the surface area of the sphere, the rest of the substitution and calculation part is easy. They can ask the same question for a circular cone, cube, right pyramid etc. So remember the basic surface area formula of these. Surface area and curved surface area are different. In the sphere both curved surface area and total surface area are the same. Which differ for other three dimensional figures.