Question

Find the surface area of the cylinder to the nearest whole number. The figure is not drawn to

scale.

905 in2
1282 in2
2187 in2
7691 in2

pls help need to pass test!!!! just struggling

Answer 1

2187

Explanation:

Answer 2

correct option is 2187

Total surface area is 2,185.44 square inches.

lateral surface area is 640.56 square inches

Explanation:

Given

radius of cylinder = 12 inches

height of cylinder = 17 inches

we will us value of pi as 3.14

surface area for cylinder consist of two part

1. lateral surface area which is gven by
`2\pi rl`

where r is radius of cylinder and l is height of cylinder

Thus, lateral surface area for given cylinder is

`2\pi rl\\ =>2* 3.14*12*17\\=> 1281.12`

Thus, lateral surface area for given cylinder is 1281.12 square inches.

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second part of surface area is area of two base (upper and lower) of cylinder.

area of base is given by area of circle
`\pi r^2`

`area \ of \base = \pi r^2 = 3.14*12^2\\=>area \ of \base = 3.14*144 = 452.16`

This, area of base is for one base of cylinder

since there are 2 base

area of both base will be = 2* area of one base

= 2*452.16 = 904.32.

Thus, area of base is 904.32 sq. in.

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Total surface area of cylinder = area of two base+ lateral surface area of cylinder = 1281.12 square inches + 904.32 square inches

= 2,185.44 square inches.

Thus, total surface area is 2,185.44 square inches.

lateral surface area is 640.56 square inches

but option which is closest to calculated value is 2187.

Thus, correct option is 2187

___________________________________________

Note: this problem can be directly solved using formula

total surface area for cylinder =
`2\pi r^2 + 2\pi rl`