Chapter 12.6, Problem 38PPS

To determine

Find the greater volume from both the figures.

Answer to Problem 38PPS

The volume of sphere and cylinder are $1375.3f{t}^3$ & $402f{t}^3$ .

Explanation of Solution

Given:

It is given in the question that there is a sphere with radius of $2.3$ yards and a cylinder with a radius of $4$ feet and height of $8$ feet.

Concept Used:

In this, use the concept of volume of sphere and the cylinder i.e. $V_{SPHERE}=\frac{4}{3}\pi r^3,V_{cylinder}=\pi r^{2}h$ .

Calculation: Here, radius of sphere = $\frac{2.3yd}{1}\times \frac{3ft}{1yd}=6.9ft$

Radius of sphere = $4$ ft and height = $8$ ft

Now, find the volume,

  $V_{SPHERE}=\frac{4}{3}\pi r^3=\frac{4}{3}\pi {(6.9)}^3=\frac{4}{3}\pi (328.5)=1375.3f{t}^3$

  $V_{cylinder}=\pi r^{2}h=\pi {(4)}^2(8)=\pi (128)=402f{t}^3$

Conclusion:

The volume of sphere and cylinder are $1375.3f{t}^3$ & $402f{t}^3$ .