A right cylinder has a circumference of 16π cm. Its height is half the radius. What is the lateral area and the surface area of the cylinder rounded to the nearest tenth?

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A right cylinder has a circumference of 16π cm. Its height is half the radius. What is the lateral area and the surface area of the cylinder rounded to the nearest tenth?

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Answer 1 · 2018-08-04T06:01:50

$L S A of cylinder = 2 π r h = 64 π \approx 201.1 c m^{2}$ $color(green)(L S A " of cylinder " = 2 pi r h = 64pi ~~ 201.1cm^2$

$T S A = L S A + A_{t b} = 64 π + 128 π = 192 π \approx 603.2 c m^{2}$ $color(chocolate)(T S A = L S A + A_(tb) = 64pi + 128 pi = 192 pi ~~ 603.2 cm^2$

Explanation:

$Circumference = C = 2 π r = 16 π c m$ $"Circumference " = C = 2 pi r = 16 pi cm$

$r = \frac{16}{2} = 8 c m$ $r = 16 / 2 = 8 cm$

$Height h = \frac{r}{2} = \frac{8}{2} = 4 c m$ $"Height " h = r/2 = 8 / 2 = 4cm$

$Lateral Surface Area of cyl. L S A = 2 π r h = 2 π \cdot 8 \cdot 4 = 64 π c m^{2} \approx 201.1 c m^{2}$ $"Lateral Surface Area of cyl. " L S A = 2 pi r h = 2 pi * 8 * 4= 64pi cm^2 ~~ 201.1 cm^2$

$Top+Bottom Area of cyl = A_{t b} = 2 π r^{2} = 2 π 8^{2} = 128 π c m^{2}$ $"Top+Bottom Area of cyl" = A_(tb) = 2 pi r^2 = 2 pi 8^2 = 128pi cm^2$

$Total Surface Area of cyl = T S A = L S A + A_{t b}$ $"Total Surface Area of cyl" = T S A = L S A + A_(tb)$

$T S A = 64 π + 128 π = 192 π \approx 603.2 c m^{2}$ $T S A = 64pi + 128pi = 192 pi ~~ 603.2 cm^2$

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A right cylinder has a circumference of 16π cm. Its height is half the radius. What is the lateral area and the surface area of the cylinder rounded to the nearest tenth?

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