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A company manufactures cylindrical cans. Each can has a volume of 9p cubic centimetres and a height of 4 centimetres. The diameter of the can is 3. use 3.14 as pi. The company plans to manufacture a can with a volume that is 25% larger than

the original can. What is the radius of the new can if the height remains the same?
Round your answer to the nearest tenth.

User Icon for Bot Bot answered
1 year ago

The original can has a diameter of 3 cm, so it has a radius of 1.5 cm.

The volume of the original can is 9p cubic cm, which means its radius cubed is 2p.
To increase the volume by 25%, we can multiply the radius cubed by 1.25:
2p * 1.25 = 2.5p
Now we solve for the new radius by taking the cube root of 2.5p and rounding to the nearest tenth:
radius = (2.5p)^(1/3) ≈ 1.4 cm.

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

To find the radius of the new can, we can use the formula for the volume of a cylinder:

Volume = π * r^2 * h

where π is approximately 3.14, r is the radius, and h is the height.

Let's start by finding the volume of the original can:

Volume = 9p cubic centimeters

Since the height is given as 4 centimeters, we can substitute these values into the formula:

9p = 3.14 * r^2 * 4

Simplifying the equation, we have:

9p = 12.56 * r^2

To find the new volume that is 25% larger than the original can, we need to multiply the original volume by 1.25:

New Volume = 1.25 * 9p = 11.25p cubic centimeters

Now, we can set up the equation for the new volume using the same formula:

11.25p = 3.14 * r^2 * 4

Simplifying this equation, we have:

11.25p = 12.56 * r^2

To find the radius, we can rearrange the equation:

r^2 = (11.25p) / 12.56

r = sqrt((11.25p) / 12.56)

Now, let's substitute the value of π as 3.14 and round the answer to the nearest tenth:

r ≈ sqrt((11.25 * 3.14) / 12.56) ≈ sqrt(8.8536 / 12.56) ≈ sqrt(0.7055) ≈ 0.839

Therefore, the radius of the new can, when the height remains the same, is approximately 0.839 centimeters.