How much chocolate is in a spherical chocolate truffle with a radius of 12 mm? Use 3.14 as an approximation for pi. Round your answer to the nearest hundredth, if necessary.(1 point
To calculate the volume of the spherical chocolate truffle, we can use the formula:
Volume = (4/3) * π * r^3
Plugging in the given radius of 12 mm and using 3.14 as an approximation for π:
Volume = (4/3) * 3.14 * (12)^3
= (4/3) * 3.14 * 1728
= 7238.08 mm³
Therefore, there is approximately 7238.08 mm³ of chocolate in the spherical chocolate truffle.
The volume of a container measures 3,200 in.3 and contains a dozen tennis balls. Each tennis ball has a radius of 2.5 in. How much space in the container is empty? Use 3.14 as an approximation for pi.
Use the formula for the volume of a sphere to find the volume of a basketball that has a diameter of 9.2 inches. Use 3.14 as an approximation for pi and round your answer to the nearest hundredth, if necessary.
The formula for the volume of a sphere is given by:
Volume = (4/3) * π * r^3
Given the diameter of the basketball is 9.2 inches, the radius (r) can be calculated by dividing the diameter by 2:
r = 9.2 inches / 2
= 4.6 inches
Plugging in the given radius of 4.6 inches and using 3.14 as an approximation for π:
Volume = (4/3) * 3.14 * (4.6)^3
= (4/3) * 3.14 * 97.336
= 408.619 in³ (rounded to the nearest hundredth)
Therefore, the volume of the basketball is approximately 408.619 in³.
To calculate the volume of a single tennis ball, we can use the formula:
Volume = (4/3) * π * r^3
Plugging in the given radius of 2.5 in and using 3.14 as an approximation for π:
Volume = (4/3) * 3.14 * (2.5)^3
= (4/3) * 3.14 * 15.625
= 65.38 in³ (rounded to the hundredth)
Since there are a dozen tennis balls, the total volume occupied by the tennis balls is:
Total volume of tennis balls = 12 * 65.38 in³
= 784.56 in³ (rounded to the hundredth)
To find the space in the container that is empty, we subtract the volume of the tennis balls from the volume of the container:
Empty space = Volume of container - Total volume of tennis balls
= 3200 in³ - 784.56 in³
= 2415.44 in³ (rounded to the hundredth)
Therefore, approximately 2415.44 in³ of space in the container is empty.