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 3vπ cubic meters (m3) 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 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 3vπ cubic meters (m3) of stone from the cylinder in order to be left with the sphere. What is the value of v ?
Given information of Sphere:The formula for the volume of a sphere is V=34πr3, where r is the radius of the sphere.Mindy's sphere has a radius of 1m, so we substitute r=1m into the formula.
Substitute Radius into Sphere Formula: Now we calculate the volume of the sphere using the radius.V=34π(1)3=34π cubic meters.
Given information of Cylinder:The formula for the volume of a cylinder is V=πr2h, where r is the radius and h is the height of the cylinder.Mindy's cylinder has a radius of 3m and a height of 2m, so we substitute r=3m and h=2m into the formula.
Substitute Radius and Height into Cylinder Formula: Now we calculate the volume of the cylinder.V=π(3)2×2=π×9×2=π×18=18π cubic meters.
Subtraction of two Volumes:18π−34π=354−4π=350πThe value of v in the expression 3vπ cubic meters is the coefficient that, when multiplied by 31π, will give us the volume of the sphere.Since we have found the difference of volumes to be 350π cubic meters, we can set up the equation:3vπ=350π
Solve for the value of v: To find the value of v, we multiply both sides of the equation by π3 to isolate v. v=(350)π×(π3)=50So, the value of v is 50.