Question

If the volume of a sphere is $7241\dfrac{1}{4}cu.cm$ , then find the radius .$\left( {take{\text{ }}\pi {\text{ = }}\dfrac{{22}}{7}} \right)$

Answer 1

Hint-In these types of questions, it is the best way to equate the volume of the sphere keeping the radius unknown . After cancelling out the common terms find the unknown radius from the equation to get the required answer .

Complete step-by-step answer:
Let r and V be the radius and volume of the solid sphere respectively .
Given V=$7241\dfrac{1}{4}cu.cm$
Since the volume of a sphere = $\dfrac{4}{3}\pi {r^3}$
$
   \Rightarrow \dfrac{4}{3}\pi {r^3} = \dfrac{{50688}}{7} \\
   \Rightarrow \dfrac{4}{3} \times \dfrac{{22}}{7} \times {r^3} = \dfrac{{50688}}{7} \\
   \Rightarrow {r^3} = \dfrac{{50688}}{7} \times \dfrac{3}{4} \times \dfrac{7}{{22}} \\
   \Rightarrow {r^3} = 1728 = {\left( {4 \times 3} \right)^3} \\
   \Rightarrow r = 12cm \\
$

Note- Always remember to recall the formulas of volume of closed 3-d figures like spheres to solve such types of questions . Remember to find the factors in the last steps if the cube root has to be found . Taking common factors outside helps to simplify the calculations to a great extent .