Cost of whitewashing a sphere is 1232₹ at the rate of 2₹/cm^2. What is the volume of a sphere? (Take π = \(\frac{22}{7}\))
A. \(\frac{4324}{3}\)
B. \(\frac{4317}{5}\)
C. \(\frac{4312}{3}\)
D. \(\frac{4312}{7}\)
This question was addressed to me in an interview for job.
I would like to ask this question from Volume of a Sphere topic in division Surface Areas and Volumes of Mathematics – Class 9
Right answer is C. \(\frac{4312}{3}\)
The explanation is: Area of a sphere = \(\frac{Total \,cost \,of \,whitewashing}{Rate \,of \,whitewashing/cm^2}\)
= \(\frac{1232}{2}\)
= 616 cm^2
We know that total surface area of a sphere = 4πr^2
4πr^2 = 616
r^2 = \(\frac{616*7}{22*4}\)
= 49
Therefore, r = 7cm
Now, volume of a sphere = \(\frac{4}{3} πr^3\)
= \(\frac{4}{3} * \frac{22}{7}\) * 7^3
= \(\frac{4312}{3}\).