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

2656.31

Step-by-step 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 = x (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 = x

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 = x diameter

diameter = 29.3

C = 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

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b