HW #12: 1) radius = 3
4) V = 36π ft3
2) radius = 2
3) a. 2:3
5) 0 (bad question!)
6) a. 20860 balls b. 1024 balls
c. 323 = 32,768
d. 243 - 32,768(9/128)π ≈ 6585.8 in3
6585.8 x .004329 ≈ 28.5 gal
b. 2:3
Review Aims 1-12
Geometry H - Use looseleaf paper where necessary.
Name:
1. For each pair of similar figures, write the ratio of side lengths a:b or c:d that
compares one pair of corresponding sides. Then write the ratios that compares
the areas of the similar figures. Simplify ratios.
Rect. C ~ Rect. D
a.
b.
2. The pyramid on the right has a scale factor of 3:1 to the left pyramid. What is
the volume of the right pyramid?
V = 5 m3
3. What is the scale factor of the two similar cylinders?
V = 729 in3
V = 64 in3
4. Find the area of the shaded regions in terms of pi and to the nearest tenth:
a.
b.
20 in.
8 cm
20 in.
5. If a square pyramid is sliced parallel to its base, the remaining bottom portion
of the pyramid is the frustum. Find its volume.
6. Find the total area to the nearest tenth:
(3x - 2) ft
5x ft
(2x + 1) ft
7. Find the total area, in simplest radical form and to the nearest cm.
9 cm
1200
10 cm
14 cm
5 cm
5 cm
34 cm
8. a. The intersection of two distinct lines is a _______________.
b. The intersection of two distinct planes is a _______________.
Always, sometimes, or never?
c. Three planes intersect in a line. __________
d. Two planes intersect in a point. __________
e. A line and a plane intersect in a point. __________
Ex. 9
9. a. Name the intersection of planes ABD and ABC: __________
b. Point C is the intersection of _________ and __________.
10. Use the diagram to answer true or false:
a. FG intersects plane ABD at point O. _____
b. A, O, and D are collinear. _____
c. F, O, and G are collinear. _____
d. D, B, and C are coplanar. _____
e. F, B, and G are coplanar. _____
f. If another plane, N, intersected plane M, the intersection would be a point. ___
11. A 3 × 5 rectangle is revolved about one of its sides of length 5 to create a solid of
revolution. Find the exact volume of the solid.
12. A 3-4-5 right triangle is revolved about a leg of length 4 to create a solid of
revolution. Describe the solid.
13. Find, to the nearest inch, the volume of the oblique cylinder with
circumference of the base 6.8π in. and height of the prism 8.3 in.
8.3 in.
14. Which figure has the greatest area?
15 in.
13 in.
18 in.
9 in.
15. Find the volume of a right triangular prism with base an isosceles right triangle
with longest side 16 mm. The height of the prism is 15 mm.
16. Find the area of the base of a right rectangular prism that has a height of
10.2 in. and a volume of 550.8 in3.
17. A right cone has a slant height of 13 feet and a diameter of 10 feet. Find the
volume of the cone in terms of π.
18. A regular pyramid with a square base is shown in the diagram below. A side,s, of
the base of the pyramid is 8 meters, and the height, h, is 18 meters. What is the
volume of the pyramid in cubic meters?
19. In a solid hemisphere, a cone is removed as shown. Calculate the volume of the
resulting solid in terms of pi.
20. Find the lateral area and total surface area of the prism below.
21. The Great Blue Hole is a cylindrical trench located off the coast of Belize. It
is approximately 1000 feet wide and 400 feet deep. about how many gallons of
water does the Great Blue Hole contain? (1 ft3 ≈ 7.48 gallons)
22. Rice falling from an open bag piles up into a figure conical in shape with an
approximate radius of 5 cm.
a) If the angle formed by the slant of the pile with
the base is roughly 300, write an expression that
represents the volume of the rice in the pile.
b) If there are approximately 20 grains of rice in a cubic centimeter,
approximately how many grains of rice are in the pile?
23. The area of the base of a cone is 24π in2 and the height is 8 in. Find the
exact area of a cross-section that is a distance of 2 units from the vertex.
24. Find the surface area of a sphere with circumference 12π ft., to the nearest
hundredth.
25. Find the volume of a sphere, to the nearest hundredth, if its surface area is
324π cm2.
26. Find the volume of the space, outside the hemisphere,
but within the cylinder. (answer in terms of π)
10 in.
2 in.