Chapter 12.3, Problem 3CYP

To determine

To calculate: The volume of the plastic building block,

  

Answer to Problem 3CYP

The volume of the plastic building block is $247.1{\text{ in}}^3$ .

Explanation of Solution

Given information:

The image of plastic building block,

  

Formula used:

The volume of a cuboid with length l, breadth b and height h is $V=lbh$ and volume of cylinder is $\pi r^{2}h$ where r is radius and h is height.

Calculation:

Consider the image of plastic building block,

  

Observe that the block has a cuboidal base and two cylinders at top.

Dimensions of cuboid are length us 12 inches, breadth is 5 inches and height is 4 inches.

Dimensions of cylinder are radius is $\frac{3}{2}$ inches and height is 1 inch.

Volume of the bock is the sum of volume of cuboid and cylinder.

  $\begin{array}{c}\text{volume of block}=\text{volume of cuboid}+\text{volume of cylinder}\\ =lbh+\pi r^{2}h\\ =12\left(5\right)\left(4\right)+\pi {\left(\frac{3}{2}\right)}^2\left(1\right)\\ =240+\frac{9\pi }{4}\end{array}$

Simplify if further as,

  $\begin{array}{c}\text{volume of block}=240+\frac{9\pi }{4}\\ =247.1\end{array}$

Thus, the volume of the plastic building block is $247.1{\text{ in}}^3$ .