Question

Can someone please help me with this question and explain how you got the answer?

Answer 1

Answer: The height is roughly 20 mm

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Explanation:

Let's find the area of the circular base
This circle has a radius of 12, so r = 12
Plug this into the area of a circle formula to get...
A = pi*r^2
A = pi*12^2
A = pi*144
A = 144*pi
A = 144*3.14  <<-- replace pi with 3.14
A = 452.16
The area of the circle is roughly 452.16 square mm

There are two of these faces, so 2*A = 2*452.16 = 904.32 represents the total base area

The lateral surface area is unknown. Let's call it L for now. If we add the total base area (904.32) to the lateral surface area (L), we would get the complete surface area which is given to be 2411.52

So,
904.32+L = 2411.52
904.32+L-904.32 = 2411.52-904.32
L = 1507.2

The lateral surface area is roughly 1507.2 square mm

The formula for the lateral surface area of a cylinder is
L = 2*pi*r*h
We found L = 1507.2 and we know that r = 12, so let's use this to find h

L = 2*pi*r*h
1507.2 = 2*3.14*12*h
1507.2 = 75.36*h
1507.2/75.36 = 75.36*h/75.36
20 = h
h = 20

The height is roughly 20 mm