A cylinder has a volume of 288 pi cubic meters and a height of 9 meters. What is the area of the base?
32 pi square meters
18 pi square meters
279 pi square meters
2,592 pi square meters
To find the area of the base, we can use the formula for the volume of a cylinder:
Volume = πr²h
where r is the radius of the base and h is the height of the cylinder.
Since we are given the volume and height, we can rearrange the formula to solve for the radius:
πr²h = Volume
πr²(9) = 288π
r² = 32
r = √32
r ≈ 5.66
Now, we can use the formula for the area of a circle to find the area of the base:
Area = πr²
Area = π(5.66)²
Area ≈ 100.53π
Rounding to the nearest whole number, the area of the base is approximately 101π square meters.
Therefore, none of the provided options are correct.
What is the height of a cylinder with a volume of 936 pi cubic inches and a diameter of 24 inches?
1.625 inches
4.75 inches
6.5 inches
39 inches
We can start by finding the radius of the cylinder using the given diameter:
radius = diameter / 2 = 24 inches / 2 = 12 inches
Next, we can use the formula for the volume of a cylinder to find the height:
volume = πr²h
Given that the volume is 936π cubic inches and the radius is 12 inches, we can rearrange the formula:
936π = π(12)²h
936π = 144πh
h = 936π / 144π
h = 6.5 inches
Therefore, the height of the cylinder is 6.5 inches.
Which is the correct first step in finding the area of the base of a cylinder with a volume of 140 pi cubic meters and a height of 12 meters?
V = B h. 12 = B (140 pi)
V = B h. V = 140 pi + (12)
V = B h. V = 140 pi (12)
V = B h. 140 pi = B (12)
The correct first step in finding the area of the base of the cylinder is to use the formula for the volume of a cylinder:
V = πr²h
where V is the volume, r is the radius of the base, and h is the height of the cylinder.
In this case, we are given the volume (140π cubic meters) and the height (12 meters). To find the radius and ultimately the area of the base, we need to rearrange the formula:
140π = πr²(12)
Now, we can solve for the radius (r) by dividing both sides of the equation by π and then by 12:
140 = r²(12)
140/12 = r²
11.67 = r²
r ≈ √11.67
r ≈ 3.42 meters (rounded to the nearest hundredth)
To find the area of the base, we can use the formula for the area of a circle:
A = πr²
A ≈ π(3.42)²
A ≈ 36.77π
Therefore, the correct first step in finding the area of the base of the cylinder with a volume of 140π cubic meters and a height of 12 meters is V = πr²h.
A paint can has a radius of 4 inches and a height of 15 inches. What is the volume of the paint can? Round to the nearest tenth. Use 3.14 for Pi.
cubic inches
The formula for the volume of a cylinder is:
Volume = πr²h
Given that the radius (r) is 4 inches and the height (h) is 15 inches, we can substitute these values into the formula:
Volume = 3.14 * (4)² * 15
Volume = 3.14 * 16 * 15
Volume = 3.14 * 240
Volume ≈ 753.6 cubic inches
Rounded to the nearest tenth, the volume of the paint can is approximately 753.6 cubic inches.