Surface area

Geometry Level 2

Find the surface area (in square feet) of the right circular cylinder shown above if the base diameter is 1.5 1.5 feet and the height is 3 3 feet. Give your answer correct to two decimal places. Use π = 22 7 \pi=\dfrac{22}{7}


The answer is 17.68.

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2 solutions

Victor Dumbrava
Sep 25, 2017

The surface area of a cylinder is:

A c y l i n d e r = 2 π r 2 + 2 π r h = 2 π r ( r + h ) A_{cylinder} = 2\pi r^2+2\pi rh=2\pi r(r+h)

Hence, the solution is quite simple:

A c y l i n d e r = 22 7 2 0.75 feet ( 0 , 75 + 3 ) feet 17.678 feet 2 A_{cylinder} = \frac{22}{7}\cdot2\cdot 0.75 \text{ feet }\cdot(0,75 + 3)\text{ feet }\approx 17.678\text{ feet}^2

The surface area is equal to the lateral area plus the area of the two bases. We have

A = 22 7 ( 1.5 ) ( 3 ) + 2 ( 22 7 ) ( 1 4 ) ( 1.5 ) 2 = A=\dfrac{22}{7}(1.5)(3)+2\left(\dfrac{22}{7}\right)\left(\dfrac{1}{4}\right)(1.5)^2= 17.68 s q u a r e f e e t \color{#D61F06}\boxed{17.68~square~feet}

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