Question

MEDAL & FAN ANYBODY ?
Find the volume of the composite space figure to the nearest whole number.
a. 546 mm.3
b. 174 mm.3
c. 364 mm.3
d. 438 mm.3

Answer 1

@Zale101 im back .

Answer 2

In your previous post, you said that the two shapes found was cylinder at the top half and a rectangular prism at the bottom half. You were correct

Answer 3

So, let's find the two volume of each of those shapes and add them up.

Answer 4

@Zale101 okay .

Answer 5

Member the volume of a rectangular prism?

Answer 6

volume=length*width*height ?

Answer 7

so its 330 ?

Answer 8

Yes,
volume=length*width*height
which means, the volume of the bottom half is 5 mm x 11 mm * x mm, which is 330 mm

Answer 9

Now, we are done calculating the volume of the bottom half of the shape. Let's move on to the top half. You said earlier that it was a cylinder. To calculate it's volume, we use the volume formula of a cylinder.

Volume of a cylinder is
\[V= \pi r^2 h\]

but, here we have the half of a cylinder. Not the full one. To find the volume of a half cylinder, we divide the actual volume by half.
Our formula will now be
\[V= (\pi r^2 h)/(2)\]

Answer 10

@Zale101 won't we need the radius ?

Answer 11

\[V=\frac{ \pi (d/2)^2 h }{ 2 }=\frac{ \pi(5/2)^2(11) }{ 2}=107.9375\]

We do need the radius, but since we have the diameter, we would half it to get the radius, i did (d/2) to get the radius. 5/2 which is 2.5. So 2.5 would be my radius, and if i plug it in the formula i would then square it.

the volume of the half cylinder is 107.9375, we round it off and get 108.0