Student’s Name Student ID No. Address
Geometry Lesson 6 Examination
Please read these instructions before you begin to answer the questions that follow.
Write your answers and your work on this examination. When you are satisfied that your answers are correct, write them on the Answer Sheet found right after the exam. Then send the Answer Sheet only (not the exam itself) to The Keystone School for grading. Attach separate paper for your work if necessary. Good Luck!
A square has an area of 100 sq. yards. What is the perimeter of the square?
Answer: ______________________
Find the area of a circle with a diameter of 10 yd.
Answer: ______________________
The base of a right rectangular prism is 10 ft. by 7 ft. The height is 3 ft. Find the surface area.
Answer: ______________________
The base of a triangular prism is an equilateral triangle with a perimeter of 42 cm. If the height of the prism is 10 cm, find the lateral area.
Answer: ______________________
If r = 4 m and h = 9 m, find the volume.
Answer: ______________________
The surface area of a cube is 96 square cm. Find the volume.
Answer: ______________________
If two solids are similar and have a linear ratio of 2:9, what is the ratio of the areas?
Answer: ______________________
The slant height of a regular pentagonal pyramid is 6 cm, and the length of each side of the base is 3 cm. Find the lateral area.
Answer: ______________________
If r = 12 in. and h = 16 in., find the slant height.
Answer: ______________________
__
__If volume = 250Π cubic yards and h = 10 yd, find the radius.
Answer: ______________________
If p = 5 and q = 3, are the spheres similar?
Answer: ______________________
12. If the ratio of areas of two similar solids is 4:9, what is the linear ratio?
Answer: ______________________
Find the area of a triangle with a base of 7 m and an altitude of 16 m.
Answer: ______________________
If r = 3 yd and h = 5 yd, find the lateral area.
Answer: ______________________
For questions 15 and 16, use the following diagram of the right cone.
If r = 4 in. and h = 3 in., find the total surface area.
Answer: ______________________
If h = 4 cm and r = 3 cm, find the volume.
Answer: ______________________
The volume of a larger prism is 168 cubic cm. If the prisms are similar with linear ratio of 3:2, what is the volume of the smaller prism?
Answer: ______________________
Find the surface area of a sphere with a radius of 9 inches.
Answer: ______________________
If volume = 24𝜋 cubic cm and r = 3, find the height.
Answer: ______________________
Find the volume of a sphere with a radius of 3 in.
Answer: ______________________
The slant height of two similar pyramids are in the ratio 1 : 5. The volume of the smaller pyramid is 60 m3. What is the volume, in cubic meters, of the larger pyramid?
Answer: ______________________
The base and height of a rectangle are both multiplied by 1/3. What is the effect on the perimeter?
Answer: ______________________
A set of points in space equidistant from a given point is called a .
In an prism, the lateral faces are rectangles and a lateral edge is an altitude.
If you slice a prism with a plane, the intersection of the prism and the plane is a __________
of the prism.
Two regular octagons have areas of 4 ft2 and 16 ft2. What is the ratio of their perimeters? a. 4:16 c. 1: 4
b. 2:4 d. 1:2
The area of a regular decagon is 50 cm2. What is the area of a regular decagon with sides four times the sides of the smaller decagon?
a. 200 cm2 b. 500 cm2 c. 800 cm2 d. 2000 cm2
A cube has a net with area 216 in2. How long is an edge of the cube?
6 in b. 15 in c. 36 in. d. 54 in.
A cylindrical can of cocoa has a radius of 7 in and a height of 5 in. What is the approximate surface area available for the label?
a. 110 in2 b. 148 in2 c. 179 in2 d. 219 in2
What is the surface area of a box that is 20.1 m long, 6.8 m wide and 7.4 m high? a. 335.7 m2 b. 411.6 m2 c. 671.5 m2 d. 721.2 m2
If the radius and height of a cylinder are both doubled, then the surface area is .
the same b. doubled c. tripled d. quadrupled
A cylinder of radius r sits snugly inside a cube. Which expression represents the difference of their lateral areas?
a. 2r2(8 – 𝜋) b. 2r(𝜋 − 2) c. 2r(4 – 𝜋) d. 4r2(4 – 𝜋)
The roof of a tower is a square pyramid with base edges 10 ft. long. The height of the pyramid is 6 ft. What is the approximate area of the roofing material needed to cover the roof?
a. 156 ft2 b. 233 ft2 c. 256 ft2 d. 333 ft2
To the nearest whole number, what is the surface area of a cone with diameter 27 m and slant height 19m?
a. 1378 m2 b. 1951 m2 c. 2757 m2 d. 3902 m2
To the nearest whole number, what is the surface area of a cone with radius 14 cm and slant height 18 cm?
a. 448 cm2 b. 836 cm2 c. 1012 cm2 d. 1407 cm2
A cylinder and a cone each have height 1 and radius √3. How does the cylinder’s lateral area x compare with the cone’s lateral area y?
x = y b. x = 2y c. x > 2y d x < 2y
A cylindrical water tank has a diameter of 9 inches and a height of 12 inches. The water surface is 2.5 inches from the top. About how much water is in the tank?
a. 604 in3 b. 636 in3 c. 668 in3 d. 763 in3
What is the volume of a rectangular prism whose edges measure 2 ft, 2ft and 3 ft? a. 7 ft3 b. 12 ft3 c. 14 ft3 d. 16 ft3
One gallon fills about 231 in3. A right cylindrical carton is 12 in. tall and holds 9 gallons when full. Find the radius of the carton to the nearest tenth of an inch.
a. 0.5 in. b. 7.4 in. c. 37.7 in. d. 55. 1in
The height of a triangle prism is 8 feet. One side of the base measures 6 feet. What additional information do you need to find the volume?
the perimeter of the base
the length of a second side of the base
the altitude of the base to the 6-foot side
the area of each rectangular face of the prism
A rectangular prism has a volume of 100 ft3. If the base measures 5 ft. by 8 ft., what is the height of the prism?
a. 2.5 ft. b. 12.5 ft. c. 20 ft. d. 40 ft.
What is the volume of a 6-ft high square pyramid with base edges 8 ft?
a. 128 ft3 b. 192 ft3 c. 256 ft3 d. 284 ft3
What is the volume of a cone with diameter 21 m and height 4 m?
a. 147 𝜋m3 b. 220.5𝜋 m3 c. 294𝜋 m3 d. 441𝜋m3
What is the volume of an oblique cone with radius 9 cm and height 12 cm?
a. 324 𝜋 cm3 b. 486 𝜋cm3 c. 648 𝜋 cm3 d. 972 𝜋cm3
If you slice an orange with a plane, the cross section will be a .
rectangle b. square c. trapezoid d. circle
A sphere with a diameter of 6 in. fits snug in a cube. What is the approximate volume of the space between the sphere and the cube?
a. 28.3 in3 b. 76.5 in3 c. 102,9 in3 d 113.1 in3
What is the surface area of a sphere whose radius is 7.5cm?
a. 75 𝜋 cm3 b. 112.5 𝜋 cm3 c. 225 𝜋 cm3 d. 562.5 𝜋 cm3
The surface area of a sphere is 576 𝜋 cm2. What is its radius?
11 cm b. 11.7 cm c. 12 cm d. 13.5 cm
The volume of a sphere is 26,244 𝜋 cm3. What is its surface area? a. 1070 𝜋 cm2 b. 1402 𝜋 cm2 c. 2448 𝜋 cm2 d. 2916 𝜋 cm2
A right triangle is revolved around the y-axis. Describe the solid of revolution.
cone b. cylinder c. sphere d. prism
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