A wedding cake is made using a cylindrical baking pan. What is the volume of a wedding cake with a diameter of 12 inches and a height of 5 inches? Round to the nearest tenth. Use 3.14 for Pi.
188.4 cubic inches
376.8 cubic inches
565.2 cubic inches
2,260.8 cubic inches
The formula to find the volume of a cylindrical shape is V = πr^2h, where V is the volume, π is approximately 3.14, r is the radius (half of the diameter), and h is the height.
In this case, the diameter is 12 inches, so the radius is 12/2 = 6 inches.
Plugging in these values into the formula, we get V = 3.14 * 6^2 * 5 = 3.14 * 36 * 5 = 565.2 cubic inches.
Therefore, the volume of the wedding cake is approximately 565.2 cubic inches. So the correct answer is 565.2 cubic inches.
The new dolphin tank at the aquarium has a radius of 75 feet and a height of 20 feet. What is the volume of the dolphin tank? Round to the nearest tenth. Use 3.14 for Pi.
9,420.0 cubic feet
88,312.5 cubic feet
94,200.0 cubic feet
353,250.0 cubic feet
The formula to find the volume of a cylindrical shape is V = πr^2h, where V is the volume, π is approximately 3.14, r is the radius, and h is the height.
In this case, the radius is 75 feet and the height is 20 feet.
Plugging in these values into the formula, we get V = 3.14 * 75^2 * 20 = 3.14 * 5625 * 20 = 353,250 cubic feet.
Therefore, the volume of the dolphin tank is approximately 353,250 cubic feet. So the correct answer is 353,250 cubic feet.
A cylinder has a volume of 140 pi cubic meters and a height of 14 meters. What is the area of the base?
10 pi square meters
12 pi square meters
126 pi square meters
1,960 pi square meters
The formula to find the volume of a cylinder is V = πr^2h, where V is the volume, π is approximately 3.14, r is the radius, and h is the height.
In this case, we are given that the volume is 140π cubic meters and the height is 14 meters. We can rearrange the formula to solve for the radius: V = πr^2h -> r^2 = V/(πh) -> r = sqrt(V/(πh)).
First, we calculate the radius: r = sqrt(140π/(π * 14)) = sqrt(10) = √10.
The formula to find the area of the base of a cylinder is A = πr^2, where A is the area and r is the radius.
Plugging in the value for the radius, we get A = π * (√10)^2 = 10π square meters.
Therefore, the area of the base of the cylinder is 10π square meters. So the correct answer is 10π square meters.
A cylinder has a volume of 315 pi cubic meters and a height of 21 meters. What is the area of the base?
15 pi square meters
18 pi square meters
294 pi square meters
6,615 pi square meters
The formula to find the volume of a cylinder is V = πr^2h, where V is the volume, π is approximately 3.14, r is the radius, and h is the height.
In this case, we are given that the volume is 315π cubic meters and the height is 21 meters. We can rearrange the formula to solve for the radius: V = πr^2h → r^2 = V/(πh) → r = sqrt(V/(πh)).
First, we calculate the radius: r = sqrt(315π/(π * 21)) = sqrt(15) = √15.
The formula to find the area of the base of a cylinder is A = πr^2, where A is the area and r is the radius.
Plugging in the value for the radius, we get A = π * (√15)^2 = 15π square meters.
Therefore, the area of the base of the cylinder is 15π square meters. So the correct answer is 15π square meters.
Healthy Grains is planning a new design for its best-selling oatmeal. It has four containers to choose from. It costs the company $0.03 per cubic inch of oatmeal to fill a container. The company does not want the new container to cost more than $4.00 to fill. Which container should the company use? Use 3.14 for Pi.
Container A Container B
A cylinder with height 7 inches and diameter 5 inches. A cylinder with height 10 inches and B = 12.57 inches squared.
Container C Container D
A cylinder with height 5.5 inches and radius 4 inches. A cylinder with height 6 inches and radius 3 inches.
container A
container B
container C
container D
To determine which container the company should use, we need to calculate the volume and cost of filling each container.
Container A:
The radius of the cylinder is half of the diameter, so the radius is 5/2 = 2.5 inches.
The volume of the cylinder is V = πr^2h = 3.14 * (2.5)^2 * 7 = 137.725 cubic inches.
The cost to fill the container is 137.725 * $0.03 = $4.13275.
Container B:
The volume of the cylinder is V = πr^2h = 3.14 * (12.57/2)^2 * 10 = 622.545 cubic inches.
The cost to fill the container is 622.545 * $0.03 = $18.67635.
Container C:
The volume of the cylinder is V = πr^2h = 3.14 * (4)^2 * 5.5 = 302.26 cubic inches.
The cost to fill the container is 302.26 * $0.03 = $9.0678.
Container D:
The volume of the cylinder is V = πr^2h = 3.14 * (3)^2 * 6 = 169.56 cubic inches.
The cost to fill the container is 169.56 * $0.03 = $5.0868.
Based on the cost to fill each container, the company should choose Container D. It is the only container that costs less than $4.00 to fill.
A soup can has a diameter of 8 cm and a height of 12 cm. What is the volume of the soup can? Use 3.14 for Pi.
A cylinder has a height of 12 centimeters and diameter of 8 centimeters.
192.00 cubic centimeters
301.44 cubic centimeters
602.88 cubic centimeters
2,411.52 cubic centimeters