Question

Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of 3000/3 Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of 3000/3 π in∧3.

One day, her sink clogged. She has to use one of two conical cups to scoop the water out of the sink. The sink is completely full when Carissa begins scooping.

(a) One cup has a diameter of 5 in. and a height of 6 in. How many cups of water must Carissa scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show all your work.

(b) One cup has a diameter of 6 in. and a height of 6 in. How many cups of water must she scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show all your work.

Answer 1

(a) Volume of 1st cup = (1/3)pi *(4/2)^2 * 8 = 32/3 pi in^3

scoops = (2000/3)pi / ( 32/3) pi = 2000/32 = 62.5 ≈ 63

(b) Volume of 2nd cup = (1/3)pi *(8/2)^2 * 8 = 128/3 pi in^3

scoops = (2000/3)pi / ( 128/3) pi = 2000/128 = 15.625 ≈ 16

I would go with the second one

it goes better with the sink

good luck

Explanation: