Question

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| Kyle draws a cone with a height of 10 inches and a radius of 3 inches.
Find the volume of each figure in the box and determine if the figure has less, equal,
or greater volume than Kyle's cone. Write the letter for each figure in the correct
column in the table.
A A cylinder with a height of 7 inches and a radius of 2 inches.
B A cylinder with a height of 30 inches and a radius of 1 inch.
C A cone with a height of 6 inches and a radius of 4 inches.
D A sphere with a radius of 3 inches.
E A sphere with a radius of 2 inches.
| Less Volume
Equal Volume | Greater Volume
a. Less Volume
b. Equal Volume
C. Greater Volume​

Answer 1

Explanation:

Given

Height of cone
`h=10\ in.`

radius of cone
`r=3\ in.`

Volume of Kyle cone

`V_k=(1)/(3)\pi r^2h`

`V_k=(1)/(3)\pi (3)^2(10)=30\ pi \ in.^3`

For cylinder A

`h=7\ in.`

`r=2\ \in.`

Volume of cylinder
`V_A=\pi r^2h`

`V_A=\pi (2)^2(7)=28\pi \ in.^3`

So,
`V_a<V_k`

Volume of cylinder
`V_B=\pi r^2h`

`h=30\ in \ r=1\ in.`

`V_B=\pi (1)^2(30)=30\pi \ in.^3`

So,
`V_B=V_k`

Volume of cone
`V_C=(\pi)/(3) r^2h`

`h=6\ in.\ r=4\ in.`

`V_A=(1)/(3)* \pi (4)^2(6)=32\pi \ in.^3`

So,
`V_C>V_k`

For sphere D

`r=3\ in.`

Volume
`V_D=(4)/(3)\pi r^3`

`V_D=(4)/(3)* \pi (3)^3=36\ \pi \ in.^3`

So,
`V_D>V_k`

For Sphere E

`r=2\ in.`

`V_D=(4)/(3)* \pi (2)^3=10.66\ \pi \ in.^3`

`V_E<V_k`