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 volume of a sphere can be calculated using the formula V = (4/3)πr³, where V is the volume and r is the radius.
Given that the radius of the scoop is 1.5 inches, we can substitute this value into the formula:
V = (4/3)π(1.5)³
V ≈ (4/3)π(3.375)
V ≈ (4/3)(3.14159)(3.375)
V ≈ 14.137
Rounding this answer to the nearest whole number, the volume of sherbet in the spherical scoop would be approximately 14 cubic inches.
How does the volume of a cylinder relate to the volume of a cone, if the cylinder and cone have the same radius?(1 point)
Responses
The cylinder's volume is 4/3 times bigger than the cone's volume.
The cylinder's volume is 4/3 times bigger than the cone's volume.
The cone's volume is 3 times larger than the cylinder's volume.
The cone's volume is 3 times larger than the cylinder's volume.
The cylinder's volume is 3 times larger than the cone's volume.
The cylinder's volume is 3 times larger than the cone's volume.
The cone's volume is 4/3 times bigger than the cylinder's volume.
The cylinder's volume is 3 times larger than the cone's volume.
A cylinder has the same radius as a sphere, and the cylinder's height is the same as the sphere's diameter. The sphere's volume is 523.6 cubic inches. What is the volume of the cylinder? (1 point)
cubic inches
The volume of a cylinder can be calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
Given that the cylinder has the same radius as the sphere, let's assume the radius of the sphere is r. Since the height of the cylinder is the same as the sphere's diameter, the height of the cylinder is 2r.
The volume of the sphere is given as 523.6 cubic inches, so:
523.6 = (4/3)πr³
We can solve this equation for r by dividing both sides by (4/3)π and then taking the cube root:
r³ = (3/4)(523.6)/π
r³ = 392.7/π
r ≈ (392.7/π)^(1/3)
Now that we have the value of r, we can calculate the volume of the cylinder:
V_cylinder = π(392.7/π)²(2(392.7/π))
V_cylinder ≈ (392.7/π)²(2(392.7/π))
V_cylinder ≈ (2(392.7/π)) × (392.7/π)²
V_cylinder ≈ (392.7/π) × (392.7/π)²
V_cylinder ≈ (392.7) × (392.7/π²)
V_cylinder ≈ 153.94
Therefore, the volume of the cylinder is approximately 153.94 cubic inches.
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The body of a rocket is made of a cylinder with a cone placed on top. The cone and cylinder have a radius of 3 inches, and the cylinder has a height of 36 inches. How much heat-resistant paint would be needed to cover the outside of the rocket?
Points awarded as follows:
1 point - Correct answer
3 points - Explanation/work shown of how answer was found
To calculate the amount of heat-resistant paint needed to cover the outside of the rocket, we need to find the surface area of both the cylinder and the cone and then add them together.
The surface area of a cylinder can be calculated using the formula A_cylinder = 2πrh, where A_cylinder is the surface area, r is the radius, and h is the height.
Given that the radius of the cylinder and cone is 3 inches and the height of the cylinder is 36 inches, we can calculate the surface area of the cylinder:
A_cylinder = 2π(3)(36)
A_cylinder = 216π
The surface area of a cone can be calculated using the formula A_cone = πrs + πr², where A_cone is the surface area, r is the radius, and s is the slant height.
The slant height of the cone can be found using the Pythagorean theorem:
s = √(r² + h²)
s = √(3² + 36²)
s ≈ 37.4833
Now we can calculate the surface area of the cone:
A_cone = π(3)(37.4833) + π(3)²
A_cone = 112.4499π
Finally, we can add the surface areas of the cylinder and cone to find the total surface area of the rocket:
A_total = A_cylinder + A_cone
A_total = 216π + 112.4499π
A_total ≈ 328.4499π
To find the amount of heat-resistant paint needed, we can simply approximate the surface area to the nearest whole number:
A_total ≈ 328 cubic inches
Therefore, approximately 328 cubic inches of heat-resistant paint would be needed to cover the outside of the rocket.