Problem 1 :
Find the surface area of a right rectangular prism with a height of 8 inches, a length of 3 inches, and a width of 5 inches.
Problem 2 :
Find the surface area of the right prism shown below.
Problem 3 :
Find the surface area of the right prism shown below.
Problem 4 :
Find the surface area of the right cylinder shown below.
Problem 5 :
Find the height of a cylinder which has a radius of 6.5 centimeters and a surface area of 592.19 square centimeters.
Problem 1 :
Find the surface area of a right rectangular prism with a height of 8 inches, a length of 3 inches, and a width of 5 inches.
Answer :
Draw a sketch.
The prism has 6 faces, two of each of the following :
The surface area of the prism is
S = 2(40) + 2(24) + 2(15)
S = 80 + 48 + 30
S = 158
So, the surface area of the right rectangular prism is 158 square inches.
Problem 2 :
Find the surface area of the right prism shown below.
Answer :
Each base measures 5 inches by 10 inches with an area of
B = 5(10)
B = 50 in^{2}
The perimeter of the base is
P = 30 in.
and the height is
h = 6 in.
The surface area is
S = 2B + Ph
S = 2(50) + 30(6)
S = 100 + 180
S = 280
So, the surface area of the right prism is 280 square inches.
Problem 3 :
Find the surface area of the right prism shown below.
Answer :
In the above prism, each base is an equilateral triangle with a side length s, of 7 meters as shown below.
Using the formula for the area of an equilateral triangle, the area of each base is
B = 1/4 ⋅ √3(s^{2})
B = 1/4 ⋅ √3(7^{2})
B = 1/4 ⋅ 49√3
B = 49√3 / 4 m^{2}
The perimeter of each base is
P = 21 m
and the height is
h = 5 m
The surface area is
S = 2B + Ph
S = 2(49√3/4) + 21(5)
S = 49√3/2 + 105
Use calculator.
S ≈ 147 m^{2}
So, the surface area of the right prism is about 147 square meters.
Problem 4 :
Find the surface area of the right cylinder shown below.
Answer :
Each base has a radius of 3 feet, and the cylinder has a height of 4 feet.
Formula for surface area of a cylinder :
S = 2πr^{2} + 2πrh
Substitute.
S = 2π(3)^{2} + 2π(3)(4)
S = 18π + 24π
S = 42π
Use calculator.
S ≈ 131.95
So, the surface area of the right cylinder is about 132 square meters.
Problem 5 :
Find the height of a cylinder which has a radius of 6.5 centimeters and a surface area of 592.19 square centimeters.
Answer :
Draw a sketch.
Formula for surface area of a cylinder :
S = 2πr^{2} + 2πrh
Substitute.
592.19 = 2π(6.5)^{2} + 2π(6.5)(4)
592.19 = 84.5π + 13πh
Subtract 84.5π from each side.
592.19 - 84.5π = 13πh
Simplify.
326.73 ≈ 13πh
Divide each side by 13π.
326.73/13π ≈ h
Use calculator and simplify.
8 ≈ h
So, the height of the cylinder is about 8 cm.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Oct 07, 22 12:25 PM
Oct 07, 22 12:20 PM
Oct 07, 22 09:38 AM