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 8 = 6 in, the height of the prism portion is h = 8 in, and the overall height is H = 13 in?

Answer 1

Given,

The length of the whole shape is 13 inches.

The length of the cuboidal part is 8 inches.

The length of the pyramid part is 13- 8= 5 inches.

The side of the base of the both part is 6 inches.

The expression for the volume of the cuboidal part is,

`V_1=l* b* h`

The expression for the volume of the pyramid part is,

`V_2=a^2+2a\sqrt{a(a^2)/(4)+h^2}`

The volume of the whole shape is,

`\begin{gathered} \text{Volume =V}_1+V_2 \\ \text{ =l}* b* h+a^2+2a\sqrt{(a^2)/(4)+h^2} \\ \text{ =8}*6*6+(6)^2+2*6\sqrt[]{(6^2)/(4)+5^2} \\ \text{ =288}+36^{}+12\sqrt[]{\frac{36^{}}{4}+25} \\ \text{ =288}+36^{}+12\sqrt[]{9+25} \\ \text{ = 288}+36^{}+12*5.83 \\ \text{ =393.971 inches}^3 \end{gathered}`

Hence, the volume of the shape is 393.971 inches cube.