Question

Calculate the surface area of the closed half-cylinder. all measurements are in cm
​

Answer 1

2656.31
`cm^(2)`

Explanation:

To calculate the surface area, we need to find the area of all the faces, and add them together.

The faces of the cylinder are: the rectangular base, the curved top, and the two semicircles on the side.

Rectangular base:

A = length x width

A = 29.3 x 16.2

A = 474.66

Two semicircles:

A =
`\pi` x
`radius^(2)` (I'm using the formula for a circle, because the two semicircles are identical, so together they form a circle)

radius = 29.3/2 = 14.65

A =
`\pi` x
`14.65^(2)`

A = 674.256 (rounded to 3 decimal places)

Curved top:

The curved top, when flattened out, becomes a rectangle with a length of 16.2. The width is equal to half the circumference of the circle formed by the two semicircles.

To find the width, use the circumference (C) formula.

C =
`\pi` x diameter

diameter = 29.3

C =
`\pi` x 29.3

C = 93.049 (rounded to 3 DP)

Area (of curved top) = length x width

A = 16.2 x 93.049

A = 1507.394 (rounded to 3 DP)

Surface Area

SA = 474.66 + 674.256 + 1507.394

SA = 2656.31
`cm^(2)`