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}`

Step-by-step explanation

Step 1

Pyramid:

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

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

then, let

heigth=12 ft

length=10 ft

now, replace.

`\begin{gathered} \text{Volume}_(pyramid)=(1)/(3)(length^2\text{)}\cdot\text{heigth} \\ \text{Volume}_(pyramid)=(1)/(3)((10ft)^2\text{)}\cdot\text{12 ft} \\ \text{Volume}_(pyramid)=(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)=(1)/(3)(\pi\cdot radius^2)\cdot\text{ heigth}`

then, Let

heigth= 8 in

radius= 6 in

now, replace.

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

I hope this helps you