Mindy is a sculptor. She has a cylinder of stone with a radius of 3 meters (m) and a height of 2m. She needs to carve out a sphere of radius 1m from the cylinder. Mindy must cut away (v)/(3)pi cubic meters (m^(3)) of stone from the cylinder in order to be left with the sphere. What is the value of v? ◻

Question

Mindy is a sculptor. She has a cylinder of stone with a radius of 3 meters  (m) and a height of 2m. She needs to carve out a sphere of radius 1m from the cylinder. Mindy must cut away (v)/(3)pi cubic meters (m^(3)) of stone from the cylinder in order to be left with the sphere. What is the value of v?  ◻

Bytelearn · Accepted Answer

Calculate Volume Formula: To find the value of v, we need to calculate the volume of the sphere that Mindy wants to carve out. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.Determine Sphere Radius: Mindy's sphere has a radius of 1m. Plugging this value into the formula for the volume of a sphere, we get V = (4/3)π(1m)^3.Calculate Volume: Calculating the volume, we have V = (4/3)π(1)^3 = (4/3)π cubic meters.Find Stone Volume: Since Mindy is carving out a sphere from the cylinder, the volume of the stone she needs to cut away is equal to the volume of the sphere. Therefore, v = (4/3)π.

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