1.) Find the height of a rectangular prism if the surface area is 148 cm2, the width is 4 cm and the length is 5 cm.

2.) Find the width of a rectangular prism if the volume is 34 cm3, the length is 1.7 cm, and the height is 0.5 cm.

3.) Find the radius of a cylinder with a volume of 118.79 feet3 and height of 5 feet.

4.) Find the surface area of the pyramid with square base that measures 8 ft by 8 ft and slant height of 12 ft.

5.) Find the slant height of a cone with surface area 63.30 ft2 and diameter 6.2 ft.

6.) Find the height of a square pyramid with volume 126.97 ft3 and dimensions of base are 6 ft by 6 ft.

7.) Find the radius of a cone with volume 199.23 cm3 and height 9 cm.

1) surface of a rectangular prism=2 (length x width) + 2 (length x height) + 2 (width x height)

Therefore:

148 cm²=2 (5 cm x 4 cm) + 2 (5 cm x h) + 2 (4 cm x h) =

148 cm²=40 cm²+10 cm h+8 cm h

18 cm h=148 cm²-40 cm²

18 cm h=108 cm²

h=108 cm² / 18 cm=6 cm.

answer: height=6 cm

2)

Volume of a rectangular prism = length x width x height

therefore:

34 cm³ = (1.7 cm) (0.5 cm) h

0.85 cm² h=34 cm³

h=34 cm³/0.85 cm²

h=40 cm.

answer: height=40 cm

3)

volume of a cylinder: πr²h

therefore.

118.79 ft³=πr² (5 ft)

r=√ (118.79 ft³/5π ft) ≈2.75 ft

answer: radius=2.75 ft

4)

Surface area of the pyramid with square base=4 (A side) + A base

A side = (1/2) (8ft) (12 ft) = 48 ft²

A base = (8 ft) (8 ft) = 64 ft²

surface area=4 (48 ft²) + 64 ft²=256 ft²

Answer: the surface area of this pyramid would be 256 ft².

5)

surface of a cone=πrs+πr²

therefore:

radius=diameter/2=6.2 ft/2=3.1 ft

63.3 ft²=π (3.1 ft) s+π (3.1 ft) ²

3.1π ft s=33.109 ft²

s=33.109 ft² / 3.1π ft

s≈3.4 ft

Answer: the slant height would be 3.4 ft.

6)

volume of a square pyramid = (area of base x heigth) / 3

therefore:

area of base = (6 ft) (6 ft) = 36 ft²

126.97 ft³=36 ft² h / 3

h=126.97 ft³/12 ft²=10.58 ft

answer: the height would be 10.58 ft.

7)

volume of a cone = (base x height) / 3

base of a cone=πr²

therefore:

199.23 cm³=πr² (9 cm) / 3

r=√ (199.23 cm³ / 3π cm) ≈4.6 cm

answer: the radius would be 4.6 cm.