v = п r 2 h # 1. the volume of a cylinder is 765 in 3. the formula for volume of a cylinder is v =...
TRANSCRIPT
V = п r2 h
# 1. The volume of a cylinder is 765 in3. Theformula for volume of a cylinder is V = п r2 h. Find the radius if the height is 4 inches. (Round to the nearest hundreth.)
ALGEBRA 1: SURFACE AREA AND VOLUME
h
Vr
2
h
Vr
414.3
765
r
56.12
765r
91.60r
r = 7.80
ALGEBRA 1: SURFACE AREA AND VOLUME
# 2. A cube has a surface area of 337.5 cm2.The formula for the surface area of a cube is SA = 6 s2. Find the side length of the cube. (Round to the nearest tenth.)
SA = 6 s2
62 SAs
6
SAs
6
5.337s
25.56s
s = 7.5
ALGEBRA 1: SURFACE AREA AND VOLUME
# 3. The volume of a sphere is 1259.83 in3.Find the radius of the sphere if the formula for fhe volume of a sphere is V = 4/3 п r3.
V = 4/3 п r3
4
33 Vr
3
4
3
V
r
3
)14.3(4
)83.1259(3r
3 914.300r
r = 6.7
ALGEBRA 1: SURFACE AREA AND VOLUME
# 4. The surface area of a sphere is 84.8 ft3.Find the radius if the formula is SA = 4 п r2.
SA = 4 п r2
42 SAr
4
SAr
)14.3(4
8.84r
56.12
8.84r
75.6r
r = 2.6
ALGEBRA 1: SURFACE AREA AND VOLUME
# 5. The circumference of an official NBAbasketball is 29.5 inches. Find the surface area using the formula: SA = 4 п r2. (Round to the nearest hundredth.)
rC 2
2
Cr
)14.3(2
5.29r
28.6
5.29r
7.4r
SA = 4 п (4.7)2
SA = 4 п (22.07)
SA = 4 п (22.07)SA = 277.34
ALGEBRA 1: SURFACE AREA AND VOLUME
# 6. The volume of a sphere is 345 mm3.Find the diameter. V = 4/3 п r3.
4
33 Vr
3
4
3
V
r
3
4
)345(3
r
3
57.12
1035r
3 34.82r
r = 4.35
d = 4.35(2) = 8.7
ALGEBRA 1: SURFACE AREA AND VOLUME
#7. Find the diameter of a can of soup if thevolume is 912 fluid ounces and the height of the can is 6.5 cm. Use the formula:V = п r2 h.
h
Vr
2
h
Vr
)5.6()14.3(
912r
41.20
912r
68.44r
r = 6.69
d = 2(6.69)= 13.37
ALGEBRA 1: SURFACE AREA AND VOLUME
#8. Find the height of a cylinder if the volumeis 2345 mm3 and the radius is 14 mm. V = п r2 h
2r
Vh
2)14(14.3
2345h
)196(14.3
2345h
44.615
2345h
h = 3.81
ALGEBRA 1: SURFACE AREA AND VOLUME
#9. What is the width of an ice cream cone thathas a volume of 170.5 cm3 and a height of8 cm? (V = 1/3 п r2 h) Round to the nearest hundredth.)
The width of the cone is the length of the diameter of the base. We
need the radius.
h
Vr
32
h
Vr
3
)8)(14.3(
)5.170(3r
12.25
5.511r
36.20r
r = 4.51
d = 2 r = 2(4.51) = 9.03
ALGEBRA 1: SURFACE AREA AND VOLUME
#10. What is the height of an ice cream cone with a volume of 213.4 cm3 and a radius of4.75 cm? (V = 1/3 п r2 h). Round to the nearesthundredth.)
2
3
r
Vh
2)75.4()14.3(
)4.213(3h
)56.22)(14.3(
2.640h
85.70
2.640h
h = 9.04