Question

Match the shapes with given dimensions to their compared volume size. (12 points)

1. Cylinder with height=10 and radius=4
a Middle volume of the three
b. Lowest volume of the three
- 2 Sphere with diameter 8
c. Highest volume of the three
3. Cone with radius-8 and height-10
a.middle volume of the three
b.lowest volume of the three
c. highest volume of the three

Answer 1

1. a. Middle volume of the three

2. b. Lowest volume of the three

3. c. Highest volume of the three

Explanation:

First lets identify the formula to find the volume of a cylinder.

V =
`\pi` r ^2 h

Now plug in the height and radius. h and r

V =
`\pi` 4^2 10

Now start solving!

V =
`\pi` 16 * 10

V =
`\pi` 160

V= 160
`\pi`

You don't really have to solve for pi here because your comparing but I'll do it anyway.

V = 502.654825

Simplify

V= 502.7

Now lets identify the formula for a sphere.

V = 4/3
`\pi` r^3

You need radius not diameter for this one [if you wanted to use diameter you can use the formula V= 1/6
`\pi` d^3 but I will show you radius].

r = d/2

r= 8/2

r=4

Plug it in

V = 4/3
`\pi` 4^3

Solve!

V = 4/3
`\pi` 64

V = 85.3333
`\pi`

V = 268.082573

Simplify

V= 268.1

We can clearly see this is less than the cylinders volume so its not the highest volume.

Lastly, the cones formula.

V =
`\pi` r^2 h/3

Plug in height and radius

V =
`\pi` 8^2 10/3

V=
`\pi` 64 * 3.3333

V = 213.3312
`\pi`

V= 670.199731

V= 670.2

This is the greatest value out of all the volumes.

So from greatest to least:

Cone

Cylinder

Sphere

If you ever need anymore help don't be afraid to reach out! Hope that helps you!