To find the height of the box, we first need to find the area of the base of the box. The area of a rectangle is length times width, so in this case the area of the base is 4 feet x 5 feet = 20 square feet.
Since there are two of these bases, we need to subtract twice the base area from the total surface area to find the area of the rest of the box:
148 sq. ft - 2(20 sq. ft) = 148 sq. ft - 40 sq. ft = 108 sq. ft
Now we need to find the area of the sides of the box. Since there are four sides, we can divide the remaining area by 4:
108 sq. ft / 4 = 27 sq. ft
Since the sides of the box are rectangles, we can use the formula for the area of a rectangle (base x height) to find the height:
4 ft x height = 27 sq. ft
height = 27 sq. ft / 4 ft = 6.75 feet
Therefore, the height of the box is 6.75 feet. None of the given options accurately represent this height, as they are all rounded numbers.
Question 4 (0.1 points)
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A new refrigerator comes packaged in a box shaped like a rectangular prism. The base of the box measures 4 feet by 5 feet. The total surface area of the box is 148 square feet.
What is the height of the box in feet?
Question 4 options:
20
18
40
6
5 answers
Question 7 (0.1 points)
A poster storage tube in the shape of a cylinder has a diameter of 3.5 inches and a volume of 122.5𝜋 cubic inches. What is the height of the poster storage tube in inches?
Question 7 options:
122.5
(1.75)2
40
3.5
A poster storage tube in the shape of a cylinder has a diameter of 3.5 inches and a volume of 122.5𝜋 cubic inches. What is the height of the poster storage tube in inches?
Question 7 options:
122.5
(1.75)2
40
3.5
To find the height of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Given that the diameter is 3.5 inches, the radius (r) is half of that, so r = 3.5 in / 2 = 1.75 inches.
We are also given the volume of the cylinder to be 122.5π cubic inches. Therefore, substituting all these values into the formula:
122.5π = π * (1.75)^2 * h
Solving for h:
122.5 = (1.75)^2 * h
122.5 = 3.0625 * h
h = 122.5 / 3.0625
h = 40
Therefore, the height of the poster storage tube is 40 inches.
The correct option is 40.
Volume = π * r^2 * h
Given that the diameter is 3.5 inches, the radius (r) is half of that, so r = 3.5 in / 2 = 1.75 inches.
We are also given the volume of the cylinder to be 122.5π cubic inches. Therefore, substituting all these values into the formula:
122.5π = π * (1.75)^2 * h
Solving for h:
122.5 = (1.75)^2 * h
122.5 = 3.0625 * h
h = 122.5 / 3.0625
h = 40
Therefore, the height of the poster storage tube is 40 inches.
The correct option is 40.
A cone has a radius of 6 centimeters and a height of 10 centimeters. What is the volume of the cone in cubic centimeters?
Question 9 options:
480π cm3
120π cm3
360π cm3
60π cm3
Question 9 options:
480π cm3
120π cm3
360π cm3
60π cm3
To find the volume of a cone, we use the formula: V = (1/3)πr^2h, where r is the radius and h is the height of the cone.
Given:
Radius, r = 6 cm
Height, h = 10 cm
Substitute the values into the volume formula:
V = (1/3)π(6)^2(10)
V = (1/3)π(36)(10)
V = (1/3)π(360)
V = (120/3)π
V = 40π
Therefore, the volume of the cone is 40π cubic centimeters.
The correct option is 40π cm3.
Given:
Radius, r = 6 cm
Height, h = 10 cm
Substitute the values into the volume formula:
V = (1/3)π(6)^2(10)
V = (1/3)π(36)(10)
V = (1/3)π(360)
V = (120/3)π
V = 40π
Therefore, the volume of the cone is 40π cubic centimeters.
The correct option is 40π cm3.
1 answer