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:

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Step3: Calculate Volume

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

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Answer:

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