Question

A storage bin has the shape of a Square Prism with a Pyramid top. What is the volume of the storage bin ifits side length is s = 3 in, the height of the prism portion is h = 11 in, and the overall height is H = 18 in?

Answer 1

Given,

The height of the shape is 18 inches.

The height of cuboidal part is 11 inches.

The height of pyramid part is 18- 11 = 7 inches.

The side of the cuboidal part is 3 inches.

The base of the pyramid part is also 3 inches.

The volume of the cuboidal part is,

`\begin{gathered} \text{Volume =l}* b* h \\ \text{Volume =s}*\text{s}* h \\ \text{ =3}*3*11 \\ \text{ =}99inches^3^{} \end{gathered}`

The volume of pyramid part is,

`\text{Volume =}a^2+2a\sqrt{(a^2)/(4)+h^2}`

Here, the value of a is 3 and h is 7 then,