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. Use the formula A=pi x radius squared x height
First, let's find the radius of the original can:
The diameter is 3, so the radius is 1.5 cm.
Using the formula for the volume of a cylinder, we can find the value of p as follows:
9p = pi x (1.5)^2 x 4
9p = 7.065
p = 7.065/9
p ≈ 0.785
Now, we need to calculate the volume of the new can:
V = 1.25 x 9p
V = 11.3125p
Using the formula A=pi x radius squared x height, and plugging in the values we know:
11.3125p = pi x r^2 x 4
r^2 = 11.3125p / (4 x pi)
r^2 ≈ 0.897
r ≈ 0.947 cm (rounded to the nearest tenth)
Therefore, the radius of the new can is approximately 0.9 cm.
To find the radius of the new can, we need to determine the new volume first.
Given that the original can has a volume of 9p cubic centimeters, the company plans to manufacture a can that is 25% larger.
To calculate the new volume, we need to add 25% of the original volume to the original volume:
New volume = Original Volume + 25% of Original Volume
New volume = 9p + (25/100) * 9p
Simplifying the above expression:
New volume = 1.25 * 9p
New volume = 11.25p
Now, we can use the formula for the volume of a cylinder to find the radius of the new can:
Volume = π * radius^2 * height
11.25p = π * radius^2 * 4
Next, rearrange the formula to solve for the radius:
radius^2 = (11.25p) / (4π)
radius^2 = (11.25 * p) / (4 * 3.14)
radius^2 = 0.897 p
Now, take the square root of both sides to find the radius:
radius = √ (0.897 p)
Calculating the value:
radius ≈ 0.948
Therefore, the radius of the new can, when the height remains the same, is approximately 0.9 centimeters (rounded to the nearest tenth).