# Question fb4b5

Feb 27, 2016

Yes, you use the formula for a cone volume to find the capacity.

depth = $\sqrt{147} \approx 12.1 c m$

capacity $\approx 622 c {m}^{3}$

#### Explanation:

$C = 2 \cdot \pi \cdot r \text{ and } V = \frac{1}{3} \cdot \pi \cdot {r}_{2}^{2} \cdot h$

Diameter$= 28 c m , \rightarrow {r}_{1} = 14 c m$

From the semicircular piece of metal we first find the circumference of the base of the cone, which is the same as ½ of the full circle,
$C = \frac{2 \cdot \pi \cdot {r}_{1}}{2}$
$C = \frac{2 \cdot \pi \cdot 14}{2} = 14 \pi \approx 44 c m$

Now find our cone radius from the cone circumference.

$C = 2 \cdot \pi \cdot {r}_{2} \rightarrow \text{ } {r}_{2} = \left(\frac{C}{2 \cdot \pi}\right)$

${r}_{2} = \frac{14 \pi}{2 \cdot \pi} = 7$

From Pythagoras, the equation for a right triangle

${r}_{1}^{2} = {r}_{2}^{2} + {h}^{2}$ we obtain:

h = sqrt(r_1^2 – r_2^2) " "rarr" " h = sqrt(196 – 49)

h= sqrt 147( ~~ 12.1 cm" "# this is the depth of the cone cup)

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

$V = \frac{1}{3} \cdot \pi \cdot 49 \cdot \sqrt{147}$

$V = 622 c {m}^{3}$ volume capacity