Question

Find the lateral surface area & volume of object in picture

Answer 1

Step-by-step explanation

In the equation, we can see that the lateral sides of the frustum are made up of trapezium.

We can extrapolate a part below.

We can find the lateral surface area using the formula below;

`\begin{gathered} \text{Lateral area = 4 }*((a+b)/(2))s \\ =4((5+11)/(2))*3.9 \\ =4((16)/(2))*3.9 \\ =4*8*3.9 \\ =124.8\text{square feet} \end{gathered}`

Answer 1: 124.8 square foot

To find the volume of the frustum we will use the formula below;

`\begin{gathered} \text{Volume of a frustrum =}(h)/(3)(a^2+ab+b^2) \\ \therefore V=(2.5)/(3)(5^2+5*11+11^2) \\ V=(2.5)/(3)(25+55+121) \\ V=(2.5*201)/(3) \\ V=2.5*67 \\ V=167.5\text{cubic f}eet \end{gathered}`

Answer 2: 167.5 cubic feet