Aaron is painting the tube of a paper towel tube for a school project. The tube is 6 inches tall and 2 inches across in diameter. He wants to know how much paint he will need to paint the outside of the tube. How many square inches is the outside of the tube? Use 3.14 for pi and round your answer to the nearest hundredth. ????? how many square inches
The circumference of the tube can be calculated by multiplying the diameter (2 inches) by pi (3.14). Therefore, the circumference is 2 * 3.14 = 6.28 inches.
To find the surface area of the tube, we need to find the area of the rectangle formed by the height of the tube (6 inches) and the circumference of the tube. The formula for the surface area of a rectangle is A = l * w, where A is the area, l is the length, and w is the width.
In this case, the length is the circumference of the tube (6.28 inches) and the width is the height of the tube (6 inches). Therefore, the area is 6.28 * 6 = 37.68 square inches.
So, Aaron will need approximately 37.68 square inches of paint to paint the outside of the tube.
What is the surface area of a cone with a slant height of 20 cm and a radius of 12 cm? Round your answer to the nearest hundredth.(1 point)
cm^2
The surface area of a cone can be calculated using the formula:
Surface Area = π * r * (r + l)
Where r is the radius of the cone and l is the slant height.
Plugging in the given values, we have:
Surface Area = 3.14 * 12 * (12 + 20)
Calculating this expression:
Surface Area = 3.14 * 12 * 32
Surface Area = 1209.6
Rounding to the nearest hundredth, the surface area of the cone is approximately 1209.6 cm^2.
Find the volume of the cylinder. Round your answer to the nearest hundredth.(1 point) the radius is 4 inches and the side is 8 inches
in3
The formula for the volume of a cylinder is given by:
Volume = π * r^2 * h
where r is the radius of the base and h is the height or side of the cylinder.
Plugging in the given values, we have:
Volume = 3.14 * 4^2 * 8
Calculating this expression:
Volume = 3.14 * 16 * 8
Volume = 401.92
Rounding to the nearest hundredth, the volume of the cylinder is approximately 401.92 in^3.
What's the volume of a cylinder with a height of 13 inches and a diameter of 7 inches? Use 3.14 for pi. Round your answer to the nearest hundredth.(1 point)
in3
To find the volume of a cylinder, we can use the formula:
Volume = π * r^2 * h
where r is the radius of the base and h is the height of the cylinder.
Given that the diameter of the cylinder is 7 inches, we can find the radius by dividing the diameter by 2:
radius = 7 inches / 2 = 3.5 inches
Plugging in the values, we have:
Volume = 3.14 * (3.5 inches)^2 * 13 inches
Calculating this expression:
Volume ≈ 3.14 * 12.25 inches^2 * 13 inches
Volume ≈ 502.57 inches^3
Rounding to the nearest hundredth, the volume of the cylinder is approximately 502.57 in^3.
Find the volume of a cone with a radius of 8 mm and a height of 20 mm. Use 3.14 for pi. Round your answer to the nearest tenth.(1 point)
mm3
The formula for the volume of a cone is given by:
Volume = (π * r^2 * h)/3
where r is the radius of the base and h is the height of the cone.
Given that the radius is 8 mm and the height is 20 mm, we can plug in these values to calculate the volume:
Volume = (3.14 * (8 mm)^2 * 20 mm)/3
Calculating this expression:
Volume = (3.14 * 64 mm^2 * 20 mm)/3
Volume = (3.14 * 1280 mm^3)/3
Volume ≈ 4227.73333 mm^3
Rounding to the nearest tenth, the volume of the cone is approximately 4227.7 mm^3.
A cone-shaped feeder has a diameter of 16 feet and a height of 12 feet. What volume can the feeder store? Round your answer to the nearest tenth.(1 point)
ft3
In order to find the volume of the cone-shaped feeder, we need to use the formula for the volume of a cone:
Volume = (π * r^2 * h)/3
where r is the radius, and h is the height of the cone.
Given that the diameter is 16 feet, we can find the radius by dividing the diameter by 2:
radius = 16 feet / 2 = 8 feet
Plugging in the values, we have:
Volume = (π * (8 feet)^2 * 12 feet)/3
Calculating this expression:
Volume = (3.14 * 64 feet^2 * 12 feet)/3
Volume = (3.14 * 768 feet^3)/3
Volume ≈ 804.17 feet^3
Rounding to the nearest tenth, the volume of the cone-shaped feeder is approximately 804.2 ft^3.
The radius of a sphere(1 point)
Responses
is the distance from the center of the sphere to any point on the surface of the sphere.
is the distance from the center of the sphere to any point on the surface of the sphere.
is the longest distance on a sphere.
is the longest distance on a sphere.
is twice the distance of the diameter.
The correct response is:
The radius of a sphere is the distance from the center of the sphere to any point on the surface of the sphere.
Find the complete surface area of a hemisphere with a radius of 14 cm. Leave your answer in terms of pi.(1 point)
Responses
392π
392pi
784π
784pi
3658.67π
3658.67pi
1829.33π
The formula for the surface area of a hemisphere is given by:
Surface Area = 2πr^2
where r is the radius of the hemisphere.
Given that the radius is 14 cm, we can plug in this value to calculate the surface area:
Surface Area = 2π(14 cm)^2
Calculating this expression:
Surface Area = 2π(196 cm^2)
Surface Area = 392π cm^2
Therefore, the complete surface area of the hemisphere with a radius of 14 cm is 392π cm^2.
If the surface area of a sphere is 457.333π
cubic centimeters, what is the radius of the sphere? Round your answer to the nearest whole number.(1 point)
centimeters
The formula for the surface area of a sphere is given by:
Surface Area = 4πr^2
where r is the radius of the sphere.
Given that the surface area is 457.333π cubic centimeters, we can set up the equation:
4πr^2 = 457.333π
Dividing both sides of the equation by 4π:
r^2 = 457.333/4
r^2 ≈ 114.333
Taking the square root of both sides:
r ≈ √114.333
r ≈ 10.7
Rounding to the nearest whole number, the radius of the sphere is approximately 11 centimeters.
How much sherbert would be in a spherical scoop if the radius of the scoop is 1.5 inches? Round your answer to the nearest whole number.(1 point)
cubic inches
The formula for the volume of a sphere is given by:
Volume = (4/3) * π * r^3
where r is the radius of the sphere.
Given that the radius of the scoop is 1.5 inches, we can plug in this value to calculate the volume:
Volume = (4/3) * π * (1.5 inches)^3
Calculating this expression:
Volume = (4/3) * π * (3.375 inches^3)
Volume ≈ 14.14 cubic inches
Rounding to the nearest whole number, the volume of the spherical scoop would be approximately 14 cubic inches of sherbet.