Geometry 10R
Name_______________________
Hw 14
1. Larry wants to make gold spherical earrings that are made from gold that has a
density of 19.3 g/cm3. If he has a gold bar that weighs 2.3 kg that he will melt
down into the earrings, what is the maximum number of pairs of spherical
earrings that have a diameter of 1.5 cm that Larry can produce to sell?
V(2 earrings) = 4/3π(.75)3(2)
≈ 3.534
D = M/V
19.3 = 2300
V
V(bar) = 2300 ≈ 119.1710 cm3
19.3 Number of earring pairs = 119.1710/.3.534 ≈ 33.718
Answers: 33 pairs
2. A company uses rectangular boxes to package small electronic components
for shipping. The box that is currently used can contain 500 of one type of
component. The company wants to package twice as many pieces per box.
Michael thinks that the box will hold twice as much if its dimensions are
doubled. Shawn disagrees and says that Michael‛s idea provides a box that
is much too large for 1,000 pieces. Explain why you agree or disagree with
one or either of the boys. What would you recommend to the company?
2h
h
l
V = lwh w
2l
2w
V = (2l)(2w)(2h)
= 8lwh I agree with Shawn.
The bigger box would have 8 times the volume. Use two of the current boxes, or just double one of the dimensions. For questions 3 and 4:
Find the volume inside the larger prism, but outside the smaller prism.
2 in.
1 ft.
3 in.
3.
1.5 ft.
4.
t.
5 f
6 ft.
6 in.
5 in.
8 in.
9 ft.
V(big prism) = 40(6) = 240 in
3
V(big prism) = 45(6) = 270 ft3
V(small prism) = 6(6) = 36 in3
V(small prism) = 1.5(6) = 9 ft3
Answer: 204 in3
5.
Find the volume to the nearest in3
of the composite solid below with a
square base with an edge of 4 in.
Answer: 261 ft3
6.
V(half­cylinder) = ½πr2h = ½π(22)(4)
= 8π
Volume(cube) = 64 in3 8π + 64 ≈ 89 in3
A compound solid is shown below.
The height of the entire solid is
20 inches and the diameter of the
solid is 10 inches. If the slant
height of the cone is 13 inches,
find the volume of the compound
solid in terms of π.
V(cone) = 1/3(25π)(12) = 100π Volume(cylinder) = (25π)(8) = 200π 300π in3
12"
5"
20 in
8"