MATH SOLVE

7 months ago

Q:
# A trash can manufacturing company makes trash cans with the dimensions shown. They also make larger cans in which the radius and the height are doubled. Which statement best describes the relationship between the volumes of the trash cans?A)The volume of the large trash can is twice the volume of the small trash can.B)The volume of the large trash can is four times the volume of the small trash can.C)The volume of the large trash can is six times the volume of the small trash can.D)The volume of the large trash can is eight times the volume of the small trash can.

Accepted Solution

A:

Hi there! The answer is D.

The volume of this cylinder can be found with the formula

[tex]v = \pi \: r {}^{2} \: h[/tex]

With r representing the radius.

The smaller can (with radius 1 and height 3), therefore has a volume of

[tex]v = \pi \times 1 {}^{2} \times 3 = 3\pi[/tex]

The larger can (with a radius of 2 × 1 = 2 and a height of 2 × 3 = 6), therefore has a volume of

[tex]v = \pi \times 2 {}^{2} \times 6 = 24\pi[/tex]

[tex]24\pi = 8 \times 3\pi[/tex]

And therefore answer D. is correct: The volume of the large trash can is eight times the volume of the small trash can.

The volume of this cylinder can be found with the formula

[tex]v = \pi \: r {}^{2} \: h[/tex]

With r representing the radius.

The smaller can (with radius 1 and height 3), therefore has a volume of

[tex]v = \pi \times 1 {}^{2} \times 3 = 3\pi[/tex]

The larger can (with a radius of 2 × 1 = 2 and a height of 2 × 3 = 6), therefore has a volume of

[tex]v = \pi \times 2 {}^{2} \times 6 = 24\pi[/tex]

[tex]24\pi = 8 \times 3\pi[/tex]

And therefore answer D. is correct: The volume of the large trash can is eight times the volume of the small trash can.