Problem 1 :
A can of baked beans has a paper label wrapped around
the outside. The can has a height of 11 cm and radius of 4.5 cm. The label
covers the entire height of the can. The label has a 1 cm overlap vertically so
that it can be stuck together calculate the area of the label
Solution :
By observing the figure,
Radius r = 4.5 cm
Height h = 11 cm
The label has a 1 cm overlap vertically. So, height h = 12 cm
Area of the label = 2πrh
= 2 × π × 4.5 × 12
= 2 × 3.14 × 4.5 × 12
= 339.12 cm
Area of the label is 339.12 cm.
Problem 2 :
The cylinder and cube below have the same surface area.
Find the side length of the cube, x.
Solution :
Radius r = 5.5 cm, height h = 4 cm
Surface area of the cylinder = surface area of the cube
2πr(h + r) = 6s^{2}
2π(5.5)(4 + 5.5) = 6(x^{2})
(11π)(9.5) = 6x^{2}
104.5π = 6x^{2}
104.5π/6 = x^{2}
17.4π =x^{2}
17.4 × 3.14 =x^{2}
54.636 = x^{2}
√54.636 = x
7.39 cm = x
So, length of cube is 7.39 cm.
Problem 3 :
A tank on the road roller is filled with water to make
the roller heavy. The tank is a cylinder that has a height of 6 feet and a
radius of 2 feet. One cubic foot of water weighs 62.5 pounds. Find the weight
of the water in the tank
Solution :
height of the tank = 6 feet, radius = 2 feet
Volume v = πr^{2}h
= 3.14 × (2)^{2} × 6
= 3.14 × 4 × 6
= 75.36 ft
So, the weight of the water in the tank is 75.36 ft.
One cubic foot of water weighs = 62.5 pounds
= 62.5 × 75.36
= 4710 pounds.
Problem 4 :
A cylinder has a surface area of 1850 square meters and a radius of 9 meters. Estimate the volume of the cylinder to the nearest whole number.
Solution :
Surface area of the cylinder = 1850 square meters
Radius = 9 meters
Surface area of the cylinder = 2πrh
1850 = 2 × 22/7 × 9 × h
1850 × 1/2 × 7/22 × 1/9 = h
32.7 = h
Volume of the cylinder V = πr^{2}h
= 22/7 × (9)^{2} × 32.7
= 8316.918 cubic meters
Problem 5 :
Water flows at 2 feet per second through a pipe with a diameter of 8 inches. A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water.
a) what is the volume, in cubic inches, of water flowing out of the pipe every second.
b) What is the height, in inches, of the water in the tank after 5 minutes?
c) How many minutes will it take to fill 75% of the tank?
Solution :
Diameter d = 8 feet ==> radius = 4 feet
height (h) = 2 feet ==> 24 inches
(a) Volume of water flows out every second = πr^{2}h
= π x 4^{2} x 24
= 384π
Using π = 3.14, we get
= 1206 cubic inches
(b) quantity of water in the cylindrical tank after 5 minutes :
5 minutes = 300 seconds
Quantity of water = 384π x 300
= 115200π
Volume of water in cylindrical tank = 115200π
πr^{2}h = 115200π
r = 15/2 ==> 7.5 feet ==> 90 inches
π(90)^{2 }h = 115200π
h = 115200/8100
h = 14.2 inches
c) How many
minutes will it take to fill 75% of the tank?
Capacity of the tank = πr^{2}h
r = 90 inches, h = 6x12 ==> 72 inches
= π(90)^{2}(72)
= 583200π
75% of the capacity = 0.75 (583200π)
= 437400π
Volume of water in 1 second = 384π
= 437400π/384π
= 1140 seconds
Converting seconds to minutes,
= 1140/60
= 19 minutes
Problem 6 :
A cylindrical swimming pool has a diameter of 16 feet and a height of 4 feet. About how many gallons of water can the pool contain? Round your answer to the nearest whole number. (1 ft^{3} ≈ 7.5 gal)
Solution :
Diameter (d) = 16 feet, radius r = 8
Height h = 4 feet
Volume of the cylinder V = πr^{2}h
= 3.14 × 8^{2} × 4
= 3.14 × 64 × 4
= 803.8 ft
1 ft^{3} = 7.5 gallon
Quantity of water that pool can contain = 7.5 × 803.8
= 6028.5 gallons
= 6029 gallons
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM