Question

the surface area of this cone is 785 square inches. what is the slant height of this cone? round your answer to the nearest hundredth. 10 in s ≈ inches

Explanation:

Step1: Recall the formula for the surface area of a cone

The surface area \( SA \) of a cone is given by \( SA=\pi r^{2}+\pi r s \), where \( r \) is the radius of the base and \( s \) is the slant height. We know that \( SA = 785 \) square inches and \( r=10 \) inches.

Step2: Substitute the known values into the formula

Substitute \( SA = 785 \), \( r = 10 \) into \( SA=\pi r^{2}+\pi r s \):

$$ 785=\pi\times(10)^{2}+\pi\times10\times s $$

Simplify \( \pi\times(10)^{2}=100\pi\approx 314.16 \) (using \( \pi\approx3.1416 \)):

$$ 785 = 314.16+31.416s $$

Step3: Solve for \( s \)

Subtract \( 314.16 \) from both sides:

$$ 785 - 314.16=31.416s $$

$$ 470.84 = 31.416s $$

Divide both sides by \( 31.416 \):

$$ s=\frac{470.84}{31.416}\approx14.99 $$

Answer:

\( s\approx14.99 \)