"A cylinder has a surface area of 748..." was answered by our community

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Answered question

2021-01-06

A cylinder has a surface area of 748 cm² and a radius of 7 cm. Estimate the volume of the cylinder to the nearest whole number.

Answer & Explanation

Laaibah Pitt

Skilled2021-01-07Added 98 answers

The surface area of a cylinder with radius r and height h is given by: $S = 2 π r h + 2 π r^{2}$
Solve for h given that $S = 748 c m^{2}$ and r=7cm:
$748 = 2 π (7) h + 2 π {(7)}^{2}$
$748 = 14 π h + 98 π$
$748 - 98 π = 14 π h$
$\frac{748 - 98 π}{14} π = h$
Using $π \sim \frac{22}{7}$ , we have: $\frac{748 - 98 (\frac{22}{7})}{14 (\frac{22}{7})} = h$
$\frac{748 - 308}{44} = h$
$\frac{440}{44} = h$
$h \sim 10 c m$
The volume of a cylinder with radius r and height h is given by: $V = π r^{2} h$
$V = π {(7)}^{2} (10)$
$V = 490 π$
Using $π \sim \frac{22}{7}$ , we have: $V = 490 \cdot (\frac{22}{7})$
$V \sim 1540 c m^{3}$

Jeffrey Jordon

Expert2021-08-10Added 2605 answers

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