# MATH HOMEWORK HELP?? *very difficult/challenging to understand (calling all GENIUSES!!)*?

A large cylindrical container with a height of 32 cm and a radius of 8 cm has water in it to a depth of 26 cm. A smaller cylindrical container with no water in it has a height of 28 cm and a radius of 5 cm. The smaller container is lowered into the larger. As it is lowered, water rises in the larger and then spills out onto the ground until the top of the smaller container is level with the top of the larger. As the smaller container is lowered further, water from the larger spills into the smaller. When the smaller container is lowered all the way, it is then removed. What is the difference, in cm, in the height of the water left in the larger container and the height of the water that spilled into the smaller?

CHOICES

A) 5.9325

B) 6.8225

C) 6.9125

D) 7.0425

E) 7.1625

### 2 Answers

- NCSLv 72 weeks agoFavorite Answer
Volume of large container:

V = πR²H = π(8cm)²*32cm = 6433.982 cm³

and initially the volume of water IN it is

Vw = π(8cm)²*26cm = 5227.610 cm³

volume of small container:

v = πr²h = π(5cm)²*28cm = 2199.115 cm³

so when the empty container is immersed so that the tops are the same height, it must be that the volume of water that spills out onto the table was

Vs = (5227.610 + 2199.115 - 6433.982) cm³ = 992.743 cm³

leaving

Vr = (5227.610 - 992.743) cm³ = 4234.867 cm³

of water remaining.

When the smaller can is immersed so that the bottoms are the same height, all of the water that HAD been below the smaller can spills into it:

Vd = πR²(H-h) = π*8²*(32-28) cm³ = 804.248 cm³

which IS less than the volume of the smaller container, so we're OK there.

That leaves a final volume in the large container of

Vf = (4234.867 - 804.248) cm³ = 3430.619cm³

height of water in small container:

h = Vd / πr² = 804.248cm³ / π(5cm)² = 10.24 cm

height of water in large container:

H = Vf / πR² = 3430.619cm³ / π(8cm)² = 17.06 cm

The difference is 6.82 cm ◄ B

Whew!

WOW! Thank you SO much! Well deserved Best Answer!!!