Question

The diagram shows a solid shape.
The volume of the cone is 270cm. V
\ 10 cm Work out the volume of the solid shape.
Give your answer in terms of t.

Answer 1

Answer:

$V=270\pi+\frac{1,024}{3}\pi=\frac{1,834}{3}\pi\ cm^3$

or

$V=611\frac{1}{3}\pi\ cm^3$

Step-by-step explanation:

step 1

Find the radius of the circular base of the cone

The volume of the cone is equal to

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

we have

$V=270\pi\ cm^3\\h=10\ cm$

substitute

$270\pi=\frac{1}{3}\pi r^{2} (10)$

simplify pi

$270=\frac{1}{3}r^{2} (10)$

$r^2=81\\r=9\ cm$

step 2

Find the volume of the hemisphere

The volume is equal to

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

we have

$r=8\ cm$ ----> is the same that the radius of the cone

substitute

$V=\frac{2}{3}\pi (8)^{3}$

$V=\frac{1,024}{3}\pi\ cm^{3}$

step 3

Find the volume of the solid shape

we know that

The volume of the solid shape is equal to the volume of a cone plus the volume of a hemisphere

so

$V=270\pi+\frac{1,024}{3}\pi=\frac{1,834}{3}\pi\ cm^3$

Convert to mixed number

$V=611\frac{1}{3}\pi\ cm^3$