Question

*hint: in general to find the volume of any prism and cylinder multiply the area of the base b the height of the prism. the height of a prism is the distance between the two bases. 3d object formula for surface area formula for volume cylinder determine the surface area and volume of the cylinders shown below. round the surface area the nearest ft² and volume to the nearest ft³.

Explanation:

Step1: Recall formulas for cylinder

The surface area \( S \) of a cylinder is given by \( S = 2\pi r^2 + 2\pi rh \), where \( r \) is the radius and \( h \) is the height. The volume \( V \) of a cylinder is given by \( V=\pi r^2h \). Here, \( r = 5\) ft and \( h = 12\) ft.

Step2: Calculate Surface Area

Substitute \( r = 5 \) and \( h = 12 \) into the surface area formula:
\[

$$\begin{align*} S&=2\pi(5)^2 + 2\pi(5)(12)\\ &=2\pi\times25+2\pi\times60\\ &=50\pi + 120\pi\\ &=170\pi\\ &\approx170\times3.1416\\ &\approx534.07 \end{align*}$$

\]
Rounding to the nearest \( ft^2 \), \( S\approx534\space ft^2 \).

Step3: Calculate Volume

Substitute \( r = 5 \) and \( h = 12 \) into the volume formula:
\[

$$\begin{align*} V&=\pi(5)^2(12)\\ &=\pi\times25\times12\\ &=300\pi\\ &\approx300\times3.1416\\ &\approx942.48 \end{align*}$$

\]
Rounding to the nearest \( ft^3 \), \( V\approx942\space ft^3 \).

Answer:

Surface Area: \(\boldsymbol{534\space ft^2}\), Volume: \(\boldsymbol{942\space ft^3}\)