Question

An ice cream company manufactures and distributes ice cream cups and cones to grocery stores. The company sells the ice cream cups in packages of 12, 18, and 24 units, and the ice cream cones in packages of 14 and 21 units. Which of the following statements is not true?

A) The 24 pack of cups has more ice cream than the 21 pack of cones.
B) The 12 pack of cups has more than 250 cubic inches of ice cream.
C) The 14 pack of cones has more than 350 cubic inches of ice cream.
D) the 12 pack of cups has enough ice cream to fill in a cylinder container, 8" tall and 6" wide.

Answer 1

Answer: A: The 24 pack of cups has more ice cream than the 21 pack of cones.

Answer 2

A) The 24 pack of cups has more ice cream than the 21 pack of cones.

Explanation:

We will find the volume of 1 cone and 1 cup.

Volume of cone :

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

r = 2 inches

h = 6 inches

V =
`3.14*2*2*(6)/(3) =25.12` cubic inches

Volume of cup :

V =
`\pi r^(2) h`

r = 1.5 inches

h = 3 inches

V =
`3.14*1.5*1.5*3=21.195` cubic inches

Now we will check the given statements:

A) The 24 pack of cups has more ice cream than the 21 pack of cones.

Volume of 24 cups =
`24*21.195=508.68` cubic inches

Volume of 21 cones =
`21*25.12=527.52` cubic inches

We can see that 24 cups have less ice cream than 21 cones. So, this statement is wrong.

B) The 12 pack of cups has more than 250 cubic inches of ice cream.

Volume of 12 cups =
`12*21.195=254.348` cubic inches

Yes, this is correct statement.

C) The 14 pack of cones has more than 350 cubic inches of ice cream.

Volume of 14 cones =
`14*25.12=351.68` cubic inches

Yes, this is correct statement.

D) the 12 pack of cups has enough ice cream to fill in a cylinder container, 8" tall and 6" wide.

Volume of cylinder with height 8 inches and radius 3 inches.

V =
`3.14*3*3*8=226.08` cubic inches

And volume of 12 cups is =
`12*21.195=254.348` cubic inches

Yes, there is enough ice cream to fill the cylinder. This is correct statement.

Therefore, option A is the only wrong option.