Question

2

James has two cans containing biscuit dough. The cans are cylindrical and their dimensions, in inches, are shown below.
8 in
A
B
4 in
H
0.5 in 1 in
Note: Figure is not drawn to scale.
Which of the following statements aboạt the volumes of the cans is true?
OA. The volumes of the two cans are equal.
ОВ.
The volume of can B is half the volume of can A.
C. The volume of can B is four times the volume of can A.
OD
The volume of can A is half the volume of can B.
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Answer 1

The volume of can A is half the volume of can B.

Explanation:

Given

Can A and Can B

Required

The true statement

For Can A, we have:

`h =8`

`r = 0.5`

The volume is:

`Volume = \pi r^2h`

This gives:

`V_A = \pi * 0.5^2 * 8`

`V_A = \pi * 2`

`V_A = 2\pi`

For Can B, we have:

`h =4`

`r = 1`

The volume is:

`Volume = \pi r^2h`

This gives:

`V_B = \pi * 1^2 * 4`

`V_B = \pi * 4`

`V_B = 4\pi`

So, we have:

`V_A = 2\pi`

`V_B = 4\pi`

By comparison, (d) is correct