2. Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of . 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 4 in. and a height of 8 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.
(b) One cup has a diameter of 8 in. and a height of 8 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.

Yes, your answers are correct.

The volume of a cone is given by V = 1/3πr²h.  Since the diameter of the first cone is 4, the radius is 2; therefore the volume is

V = 1/3π(2²)(8) = 32π/3

We divide the volume of the sink, 2000π/3, by the volume of the cone:

2000π/3 ÷ 32π/3 = 2000π/3 × 3/32π = 6000π/96π = 62.5 ≈ 63.

The diameter of the second conical cup is 8, so the radius is 4.  The volume then is:

V = 1/3π(4²)(8) = 128π/3

Dividing the volume of the sink, 2000π/3, by 128π/3:

2000π/3 ÷ 128π/3 = 2000π/3 × 3/128π = 6000π/384π = 15.625 ≈ 16

$2416.6

step-by-step explanation:

per hour = $ 25

total work time = 35

commission = 15%

total she has to make = $ 4,500

let she sold x dollar products

so her commission will be 15 % of x

now

total = weekly basic pay + commission

4500= (25*35) + 15 % of x

4500=875 + * x

4500-875 =   * x

3625= * x

multiplying wwith 100 on both sides gives

36250 = 15 x

now

x =  

x= $2416.6