SOLUTION: Write the indicated equation for each geometric solid. 1.)The surface area of a cube with an edge of x centimetres long. I got the answer s=24x 2.)The volume of a cylind

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Question 83570: Write the indicated equation for each geometric solid.

1.)The surface area of a cube with an edge of x centimetres long.
I got the answer s=24x
2.)The volume of a cylinder with an height of 5 metres and a radius of x metres.
I got the answer V=≈x^2*5 ≈ is pie (3.14).
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Find the equation for the surface area of a cube with an edge of x centimetres long.
.
Each face of the cube is a square that has a length of x cm for a side. The area of a
square is found by squaring the length of a side. So the area of a face of this given
cube is . Think about the shape of the cube. (A die is an example.) It has
a total of 6 faces ... 4 going around it plus a top face and a bottom face. Since there are
6 faces and each face has an area of , the total surface area (call it S) is given
by:
.

.
and since the given dimensions for the side of a face is in centimetres, the units of the
answer is square centimetres
.
To find the volume of a cylinder, you multiply the area of its circular base times the
height of the cylinder. The area (A) of a circle is given by the equation:
.

.
where R is the radius of the circle. In this problem you are told that the radius is
given by x, so substitute x metres for R and the equation becomes:
.

.
Then, to find the volume (V) you multiply this area by the height (H) and you get:
.

.
but you are given that the height of the cylinder is 5 m. Substituting this value for
H results in the volume equation becoming:
.

.
and since the radius and height are in metres, the units of the answer is cubic metres.
.
Hope you can track the development of each of these equations and that it helps you to
understand the problems a little better.