Mindy is a sculptor. She has a cylinder of stone with a radius of 3meters3πv and a height of 2meters. She needs to carve out a sphere of radius 1meter from the cylinder. Mindy must cut away cubic meters of stone from the cylinder in order to be left with the sphere. What is the value of v?
Q. Mindy is a sculptor. She has a cylinder of stone with a radius of 3meters3πv and a height of 2meters. She needs to carve out a sphere of radius 1meter from the cylinder. Mindy must cut away cubic meters of stone from the cylinder in order to be left with the sphere. What is the value of v?
Calculate Cylinder Volume: Calculate the volume of the cylinder:Volume of cylinder = π×radius2×height= π×(π3)2×2= π×(π29)×2= (π18) cubic meters
Calculate Sphere Volume: Calculate the volume of the sphere:Volume of sphere = (34)πradius3= (34)π13= (34)π cubic meters
Calculate Volume to Cut: Calculate the volume of stone Mindy needs to cut away:Volume to cut away = Volume of cylinder - Volume of sphere= (π18)−(34)×π= (π18)−(34π)= 3π54−4π2 cubic meters
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