What is the volume of a cone with a diameter of 20 cm and a height of 15 cm? (1 point) Responses 1,570 cubic centimeters 1,570 cubic centimeters 314 cubic centimeters 314 cubic centimeters 2,355 cubic centimeters 2,355 cubic centimeters 6,280 cubic centimeters 6,280 cubic centimeters
The correct answer is 1,570 cubic centimeters.
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 6.28 cubic centimeters 6.28 cubic centimeters 18.84 cubic centimeters 18.84 cubic centimeters 12.56 cubic centimeters 12.56 cubic centimeters 37.68 cubic centimeters
To calculate the volume of a cone, we can use the formula:
Volume = (1/3) * π * r^2 * h
Given that the diameter of the chocolate mold is 2 cm, the radius would be half of that, which is 1 cm. The height of the chocolate mold is 6 cm.
Plugging in the values into the formula:
Volume = (1/3) * 3.14 * 1^2 * 6
= (1/3) * 3.14 * 1 * 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 75.36 cubic meters 75.36 cubic meters 25.12 cubic meters 25.12 cubic meters 150.72 cubic meters 150.72 cubic meters 100.48 cubic meters 100.48 cubic meters
To calculate the volume of a cone, we can use the formula:
Volume = (1/3) * π * r^2 * h
Given that the diameter of the sandcastle mold is 4 meters, the radius would be half of that, which is 2 meters. The height of the sandcastle mold is 6 meters.
Plugging in the values into the formula:
Volume = (1/3) * 3.14 * 2^2 * 6
= (1/3) * 3.14 * 4 * 6
= 100.48 cubic meters
Therefore, the volume of sand needed to fill the mold is 100.48 cubic meters.
To find the volume of a cone, you can use the formula: V = (1/3) * π * r^2 * h, where V represents the volume, π is a mathematical constant (approximately 3.14159), r is the radius of the base of the cone, and h is the height of the cone.
Given that the diameter of the cone is 20 cm, we need to first find the radius (r). The radius is half the diameter, so the radius is 20 cm / 2 = 10 cm.
Using the formula, we can substitute the values into the equation:
V = (1/3) * π * (10 cm)^2 * 15 cm
Simplifying further:
V = (1/3) * 3.14159 * (100 cm^2) * 15 cm
V ≈ 1.04719 * 1000 cm^3
V ≈ 1047.19 cm^3
Thus, the volume of the cone is approximately 1047.19 cubic centimeters.