Question

7) Find the volume of the following shapes: (i) Pyramid (ii) Cone 8 in loft Gin loft V= V=

Answer 1

$\begin{gathered} \text{Pyramid: Volume}_{pyramid}=400ft^3 \\ Cone\colon\text{Volume}_{cone}=96In^3 \end{gathered}$

Explanation

Step 1

Pyramid:

the volume of a pyramid with square base is given by:

$\text{Volume}_{pyramid}=\frac{1}{3}(length^2\text{)}\cdot\text{heigth}$

then, let

heigth=12 ft

length=10 ft

now, replace.

$\begin{gathered} \text{Volume}_{pyramid}=\frac{1}{3}(length^2\text{)}\cdot\text{heigth} \\ \text{Volume}_{pyramid}=\frac{1}{3}((10ft)^2\text{)}\cdot\text{12 ft} \\ \text{Volume}_{pyramid}=\frac{1}{3}1200ft^3 \\ \text{Volume}_{pyramid}=400ft^3 \end{gathered}$

Step 2

Cone:

the volume of a cone is given by:

$\text{Volume}_{cone}=\frac{1}{3}(\pi\cdot radius^2)\cdot\text{ heigth}$

then, Let

heigth= 8 in

radius= 6 in

now, replace.

$\begin{gathered} \text{Volume}_{cone}=\frac{1}{3}(\pi\cdot radius^2)\cdot\text{ heigth} \\ \text{Volume}_{cone}=\frac{1}{3}(\pi\cdot(6in)^2)\cdot\text{ 8 in} \\ \text{Volume}_{cone}=\frac{1}{3}(\pi\cdot36in^2)\cdot8\text{ in} \\ \text{Volume}_{cone}=\frac{1}{3}(288\pi)In^3 \\ \text{Volume}_{cone}=96In^3 \end{gathered}$

I hope this helps you