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3 votes
3 votes
3. John and Susie are making fruit smoothies. John has a cylindrical container for his drink while Susie

has a cone for her drink. John's container has a radius of 6 inches and a height of 10 inches while

Susie's container has the same base and equal height.

a. Find the volume of each container.

b. How many times will Susie need a refill in order to have the same amount of smoothie as John?

Verify your reasoning.

c. If John finds a container that is half the height of his previous container but has the same size

base, how will the volume of John's new container compare to Susie's cone-shaped container?

User Eshalev
by
2.5k points

1 Answer

16 votes
16 votes

All we really need to pull from the paragraph are the following details:

"John has a cylindrical container ... while Susie has a cone. John's container has a radius of 6 inches and a height of 10 inches while Susie's container has the same base and equal height."

a. Find the volume of each container.

[] We can solve this by solving for the volumes via known mathematical formulas

John's Cylindrical Container is about 1,130.97 inches cubed

-> V = πr²h

-> V = π6²10

-> V ≈ 1130.97

Susie's Cone is about 376.99 inches cubed

-> V = πr²
(h)/(3)

-> V = π6²
(10)/(3)

-> V ≈ 376.99

b. How many times will Susie need a refill in order to have the same amount of smoothie as John? Verify your reasoning.

[] Let x be the number of times Susie refills her cone.

1,130.97 = 376.99x

3 = x

x = 3

Suize will refill her cone 3 times

c. If John finds a container that is half the height of his previous container but has the same size base, how will the volume of John's new container compare to Susie's cone-shaped container?

[] We will assume that John still has a cylindrical container.

[] Using the same formula from step one, we will solve for the volume of the new contaier

[] 10 / 2 = 5, so the new height is 5 inches

-> V = πr²h

-> V = π6²5

-> V ≈ 565.49

[] Now we will compare this to Suise's container

-> 565.49 - 376.99 = 188.5 inches cubed

-> 565.49 / 376.99 ≈ 1.5

John's container will be about 1.5 times larger than Suise's, or 188.5 inches cubed larger.

User Tzerb
by
3.3k points
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