CH 12

Ch 12 Study Guide A

Match each solid to its net.

2. Find the surface area of the square pyramid.

3. Find the volume of the triangular prism.

4. The area of one face of a cube is 81 square inches. Find the volume of the cube.

5. The solid below is made up of 2-inch cubes. Find the volume of the solid.

6. Find the height of the triangular prism given that its volume is 240 cubic centimeters.

7. A rectangular metal block measures 18 centimeters by 6 centimeters by 4 centimeters. It is melted down and recast into 2 identical smaller cubes. What is the edge length of each cube?

8. The ratio of the length to the width to the height of a rectangular box of cereal is 4:2:7. The sum of the length and width of the box is 18 centimeters. Find the surface area of the box of cereal.

9. A rectangular container with a base of 24 inches by 10 inches is 1/3 filled with water. If all the water is poured into an empty rectangular container, measuring 12 inches by 14 inches by 10 inches, it will fill the second container to its brim. What is the height of the first container?

ANSWER KEY

2. Find the surface area of the square pyramid.

Surface Area = base: 8x8 = 64cm²

one side = 1/2 x 12 x 8 = 48cm²

all 4 triangle faces = 48 x 4 = 192cm²

base and faces = 64 +192 = 256cm²

3. Find the volume of the triangular prism.

V = (1/2 a x b) x h

= 1/2 x 4 x 6 x 7

= 2 x 6 x7 = 12 x 7 = 84m³

4. The area of one face of a cube is 81 square inches. Find the volume of the cube.

If a cube face area is 81 sq in it has side lengths of √81 = 9. the volume of a cube of sides of 9 is: 9³or 9 x 9 x 9 = 81 x 9 = 729 in³.

5. The solid below is made up of 2-inch cubes. Find the volume of the solid.

bottom layer : 9 cubes

middle layer : 8 cubes

top layer : 4 cubes

Total 21 cubes.

1 cube has a volume of 2 x 2 x 2 = 4 x 2 = 8 in³.

21 cubes have a volume of 21 x 8 in³ = 168 in³.

6. Find the height of the triangular prism given that its volume is 240 cubic centimeters.

V = 1/2 a x b x h

240 = 1/2 x 6 x 8 x h

240 = 24 xh

h = 240/24

h = 10 in.

7. A rectangular metal block measures 18 centimeters by 6 centimeters by 4 centimeters. It is melted down and recast into 2 identical smaller cubes. What is the edge length of each cube?

18 x 6 x 4 = 432 cm³.

432/2 = 216 cm³ for each.

cube root of 216 = 6 so each side of the small cubes is 6 cm long.

8. The ratio of the length to the width to the height of a rectangular box of cereal is 4:2:7. The sum of the length and width of the box is 18 centimeters. Find the surface area of the box of cereal.

4:2:7 = l:w:h l + w = 4 +2 = 6 (ratio sum)

18 (box sum)

ratio sum x 3 = box sum, so multiply each dimension by 3!

l: 4 x 3 = 12

w: 2 x 3 = 6

h: 7 x 3 = 21

two bases surface area = lxw x2 = 12 x 6 x 2 = 144 sq.in.

two long sides surface area = h x l = 21 x 12 x 2 = 504 sq.in.

two width side surface areas = h x w = 21 x 6 x 2 = 252 sq.in.

Total surface area = 144 + 504 + 252 = 900 sq.in.

9. A rectangular container with a base of 24 inches by 10 inches is 1/3 filled with water. If all the water is poured into an empty rectangular container, measuring 12 inches by 14 inches by 10 inches, it will fill the second container to its brim. What is the height of the first container?

Vsmall = 12 x 14 x 10 = 1680 cu. in.

1/3 of big box = 1680 cu. in.

1680 = 24 x 10 x H

1680/240 = H

H = 7 in for 1/3 of the height.

height of entire big box is 7 x 3 = 21 inches.