Question

What is the volume,surface area,and the cost of material? the cardboard cost $0.05 per square inch.

Answer 1

A cardboard in the shape of a cylinder with a radius of 2.5in and a height of 12in is given.

It is required to find the volume, surface area, and cost of material if it costs $0.05 per square inch.

The Volume of a Cylinder is given as:

`V=\pi r^2h`

Substitute r=2.5 and h=12 into the formula:

`\begin{gathered} V=\pi(2.5)^2(12) \\ Use\text{ }\pi\approx3.14\text{:} \\ V=3.14(2.5)^2(12)=235.5 \end{gathered}`

Hence, the volume is 235.5 in³.

The Total Surface Area of a cylinder is:

`SA=2\pi r^2+2\pi rh`

Substitute r=2.5 and h=12 into the formula:

`\begin{gathered} SA=2\pi(2.5)^2+2\pi(2.5)(12)=12.5\pi+60\pi=72.5\pi \\ \text{Use }\pi\approx3.14: \\ SA=72.5(3.14)=227.65 \end{gathered}`

Hence, the surface area is 227.65 in².

To calculate the cost of material since the cost per square inch is given, multiply the total surface area by the cost per square inch:

`227.65*0.05=11.3825`

The cost of the material is about $11.3825.

Answer:

The volume is 235.5 in³.

The surface area is 227.65 in².

The cost of the material is about $11.3825.