To solve these problems, we can use the formula for the volume of a cylinder, which is V = π * r^2 * h, where V represents the volume, r represents the radius of the base, and h represents the height.
a) Finding the height:
Given:
- Radius (r) = 5 cm
- Volume (V) = 500 cm^3
To find the height (h), we can rearrange the formula and solve for h:
V = π * r^2 * h
500 = π * 5^2 * h
500 = 25Ï€ * h
Divide both sides of the equation by 25Ï€ to isolate h:
h = 500 / (25Ï€)
h ≈ 8 cm (rounded to the nearest whole number)
Therefore, the height of a cylinder with a radius of 5 cm and a volume of 500 cm^3 is approximately 8 cm.
b) Finding the radius:
Given:
- Volume (V) = 300 cm^3
- Height (h) = 10 cm
To find the radius (r), we rearrange the formula and solve for r:
V = π * r^2 * h
300 = π * r^2 * 10
Divide both sides of the equation by 10Ï€ to isolate r:
r^2 = 300 / (10Ï€)
r^2 ≈ 9.549 (rounded to three decimal places)
To find the radius (r), we take the square root of both sides of the equation:
r ≈ √(9.549)
r ≈ 3.09 cm (rounded to two decimal places)
Therefore, the radius of a cylinder with a volume of 300 cm^3 and a height of 10 cm is approximately 3.09 cm.