Question

lesson 5 - 3d objects: cylinders

• remember:

surface area - a measure of the amount of space that covers an entire object. surface area is measured in square units such as cm², m², in², ft², ..
volume - a measure of the amount of space an object occupies. volume is measured in cubic units such as cm³, m³, in³, ft³, ..
*hint: in general to find the volume of any prism and cylinder multiply the area of the base by the height of the prism. the height of a prism is the distance between the two bases.

determine the surface area and volume of the cylinders shown below. round the surface area to the nearest ft² and volume to the nearest ft³.
(image of a cylinder with height 12 ft and radius 5 ft)

Explanation:

Step1: Recall Cylinder Formulas

The surface area \( SA \) of a cylinder is given by \( SA = 2\pi r^2 + 2\pi rh \), 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 \( r = 5 \), \( h = 12 \) into the surface area formula:
\[

$$\begin{align*} SA&=2\pi(5)^2 + 2\pi(5)(12)\\ &=2\pi(25)+2\pi(60)\\ &=50\pi + 120\pi\\ &=170\pi\\ &\approx170\times3.1416\\ &\approx534.07 \text{ ft}^2 \end{align*}$$

\]

Step3: Calculate Volume

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

$$\begin{align*} V&=\pi(5)^2(12)\\ &=\pi(25)(12)\\ &=300\pi\\ &\approx300\times3.1416\\ &\approx942.48 \text{ ft}^3 \end{align*}$$

\]

Answer:

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