Question

find the volume of the compound shape.​

Answer 1

Volume of the hemisphere:

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

$v = \frac{2}{3} \times \pi \times {3}^{3}$

$v = 56.55 \: {cm}^{3}$

Volume of the cone:

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

$v = \frac{1}{3} \times \pi \times {3}^{2} \times 10$

$v = 94.25 \: {cm}^{3}$

Total volume:

$v = 56.55 + 94.25$

$v = 150.80 \: {cm}^{3}$

Therefore, the volume of the compound shape is 150.80 cubic centimeters.

Answer 2

half of a sphere:

=56.55 cm^3

cone:

=94.25 cm^3

all together:

150.80 cm^3