QUESTION 1
The volume of a cone is calculated using the formula,
[tex]V= \frac{1}{3} \pi \: {r}^{2} h[/tex]
The radius is r=5m.
Let, the height of the right triangle be h,
Then, Pythagoras Theorem says that, the sum of the squares of the two shorter legs is equal to the square of the hypotenuse.
[tex] {h}^{2} + {5}^{2} = {13}^{2} [/tex]
[tex]{h}^{2} + 25= 169[/tex]
[tex]{h}^{2} = 169 - 25[/tex]
[tex]{h}^{2} = 144[/tex]
[tex]h = \sqrt{144} = 12m[/tex]
We now substitute, the values to get,
[tex]V= \frac{1}{3} \times \pi \times {5}^{2} \times 12[/tex]
[tex]V= 314.2 {m}^{3} [/tex]
Question 2
This is a rectangular prism.
The formula for finding the volume of a rectangular prism is
[tex]V=l \times b \times h[/tex]
The length is 11cm
The width is 5cm
The height is 6cm.
We substitute into the formula to get,
[tex]V=11 \times 5 \times 6[/tex]
[tex]V = 330.0 {cm}^{3} [/tex]
