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:
[tex]V=\pi r^2h[/tex]
Substitute r=2.5 and h=12 into the formula:
[tex]\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}[/tex]
Hence, the volume is 235.5 in³.
The Total Surface Area of a cylinder is:
[tex]SA=2\pi r^2+2\pi rh[/tex]
Substitute r=2.5 and h=12 into the formula:
[tex]\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}[/tex]
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:
[tex]227.65\times0.05=11.3825[/tex]
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.
