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# A sphere has volume $36\pi c{{m}^{3}}$ , find the radius of the sphere?(a) 4 cm(b) 3 cm(c) 6 cm(d) 8 cm

Last updated date: 21st Jun 2024
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Hint:
We start solving the problem by assigning the variable for the radius of the given sphere. We then draw the figure representing the given information. We then recall the fact that the volume of the sphere with radius ‘r’ is defined as $\dfrac{4}{3}\pi {{r}^{3}}$ . We equate the formula to the given volume and then make the necessary calculations to get the required value of the radius of the sphere.

According to the problem, we are asked to find the radius of the sphere whose volume is $36\pi c{{m}^{3}}$.
Let us assume the radius of the sphere be ‘r’ cm.
Let us draw the figure representing the given information.

We know that the volume of the sphere with radius ‘r’ is defined as $\dfrac{4}{3}\pi {{r}^{3}}$ .
So, we have $\dfrac{4}{3}\pi {{r}^{3}}=36\pi$ .
$\Rightarrow {{r}^{3}}=36\times \dfrac{3}{4}$ .
$\Rightarrow {{r}^{3}}=27$ .
$\Rightarrow r=\sqrt[3]{27}$ .
$\Rightarrow r=3cm$ .
So, we have found the radius of the given sphere as 3 cm.
$\, therefore,$ The correct option for the given problem is (b).

Note:
Whenever we get this type of problem, we first try to assign variables to the unknowns present in the problem to avoid confusion while solving this problem. We should not confuse with the formulae of volume, surface while solving problems related to mensuration. We can also find the surface area of the given sphere using the obtained value of the radius of the sphere. Similarly, we can expect problems to find the volume of a cylinder with a height 10 cm and a radius equal to the radius of the given sphere.