Question

Mad math for pi, I have no clue how to do this!!

Answer 1

To calculate the volume of this figure, we just have to find the volume of the hemisphere and the volume of the cone, then sum them up.

The volume of a hemisphere (the half of a sphere) is given by the formula:

$V=\frac{2}{3}\pi r^3$

Where r is the radius.

The volume of a cone is given by the formula:

$V=\frac{1}{3}\pi r^2h$

Where h is the height of the cone.

From the figure we have:

r = 5.3in

h = 9 in

Then, when we substitute these values into the above formulas, we get:

For the hemisphere:

$V=\frac{2}{3}\pi r^3=\frac{2}{3}\times3.14\times(5.3)^3=311.6$

The volume of the hemisphere is 311.6in^3

For the cone:

$V=\frac{1}{3}\pi r^2h=\frac{1}{3}\times3.14\times5.3^2\times9=264.7$

As mentioned, the volume of the whole figure is the sum of the volume of the cone and the volume of the hemisphere, then, the volume of the figure is:

V=311.6in^3 + 264.7in^3 = 576.3in^3

Then, the correct answer is option A