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.
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.
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.