Question

A cylindrical vase has a diameter of 4 inches. At the bottom of the vase, there are 6 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 8 inches.

Which of the following could be used to calculate the volume of water in the vase?

π(2in)2(8in) − 6(four over threeπ(1.5in)3)
π(8in)2(2in) − 6(four over threeπ(1.5in)3)
π(2in)2(8in) − 1.5(four over threeπ(6in)3)
π(8in)2(2in) − 1.5(four over threeπ(6in)3)

Answer 1

(not to scale)

consider the water + marbles as a cylinder with height 8 inches and diameter 4 inches. the radius is diameter/2, or 4/2 = 2 inches.

volume of a cylinder: (pi)(r^2)(h), where r = 2 and h = 8. plug them in, but don't evaluate the expression yet.

volume of each sphere: (4/3)(pi)(r^3) where the radius is diameter/2 = 3/2 inches. multiply by 6 since there are 6 spheres ---> 6(4/3)(pi)(r^3) plug in this r value.

once you have both expressions, simply set up

(volume of cylinder) - (volume of spheres) and see which answer choice best matches your expression

Answer 2

still there? would you like me to clarify anything I said? I'd be happy to C: