Question

Find the surface area of the shape below. Round your answer to two decimal places.

Answer 1

The surface area of the given shape is 285.01 ft²

Surface area of a cone

From the question, we are to calculate the surface area of the given shape.

The given shape in the diagram is a cone.

The surface area of a cone is given by the formula,

$S = \pi r(r+l)$

Where S is the surface area

r is the radius

and $l$ is the slant height

First, we will calculate the slant height of the cone

$l^{2}=9^{2} +5.6^{2}$ (Pythagorean theorem)

$l^{2}=81+31.36$

$l^{2}=112.36$

$l}=\sqrt{112.36}$

$l=10.6 \ ft$

∴ The slant height is 10.6 ft

Now, for the surface area

$S = \pi \times 5.6(5.6+10.6)$
$S = \pi \times 5.6(16.2)$

$S = 90.72\pi \ ft^{2}$

$S = 285.0053 \ ft^{2}$

S ≅ 285.01 ft²

Hence, the surface area of the given shape is 285.01 ft²

Learn more on Calculating surface area of a cone here: brainly.com/question/27812847

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