A professional baker uses a chocolate mold to make decorations for cakes. One chocolate mold is in the shape of a cone and has a diameter of 2 cm and a height of 6 cm. What volume of chocolate, in cubic centimeters, is needed to make a solid chocolate cone? Use 3.14 for π
.(1 point)
Responses
37.68 cubic centimeters
37.68 cubic centimeters
6.28 cubic centimeters
6.28 cubic centimeters
18.84 cubic centimeters
18.84 cubic centimeters
12.56 cubic centimeters
The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.
In this case, the diameter of the cone is given as 2 cm, so the radius is half of that, which is 1 cm. The height is given as 6 cm.
Plugging these values into the formula, we get:
V = (1/3) * 3.14 * (1^2) * 6
= (1/3) * 3.14 * 1 * 6
= 0.33 * 3.14 * 6
= 6.28 cubic centimeters
Therefore, the volume of chocolate needed to make a solid chocolate cone is 6.28 cubic centimeters.
A sandcastle mold is in the shape of a cone, with a diameter of 4 meters and a height of 6 meters. What volume of sand is needed to fill the mold? Use 3.14 for π
.(1 point)
Responses
25.12 cubic meters
25.12 cubic meters
100.48 cubic meters
100.48 cubic meters
75.36 cubic meters
75.36 cubic meters
150.72 cubic meters
The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.
In this case, the diameter of the cone is given as 4 meters, so the radius is half of that, which is 2 meters. The height is given as 6 meters.
Plugging these values into the formula, we get:
V = (1/3) * 3.14 * (2^2) * 6
= (1/3) * 3.14 * 4 * 6
= 0.33 * 3.14 * 4 * 6
= 25.12 cubic meters
Therefore, the volume of sand needed to fill the sandcastle mold is 25.12 cubic meters.
A hanging flower vase is in the shape of a cone with a radius of 5 inches and a height of 15 inches. What volume of water can the flower vase hold? Use 3.14 for π
.(1 point)
Responses
1,177.5 cubic inches
1,177.5 cubic inches
1,570 cubic inches
1,570 cubic inches
78.5 cubic inches
78.5 cubic inches
392.5 cubic inches
The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.
In this case, the radius of the flower vase is given as 5 inches, and the height is given as 15 inches.
Plugging these values into the formula, we get:
V = (1/3) * 3.14 * (5^2) * 15
= (1/3) * 3.14 * 25 * 15
= 0.33 * 3.14 * 25 * 15
= 1,177.5 cubic inches
Therefore, the hanging flower vase can hold 1,177.5 cubic inches of water.