Use the image to answer the question.
An illustration shows a horizontal rectangle of unknown height (in meters) with a circle of diameter 12 meters attached to its top left and a circle of diameter 12 meters attached to its bottom right.
If the surface area of the net diagram of the right circular cylinder is 715.92 meters2 , find the height. Use 3.14 for π .
(1 point)
Responses
6.5 meters
6.5 meters
13 meters
13 meters
16 meters
16 meters
42 meters
42 meters
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The surface area of a right circular cylinder is calculated using the formula:
Surface Area = 2πr² + 2πrh
In this case, we are given the surface area as 715.92 meters² and the diameter of the circle attached to the rectangle is 12 meters. The radius (r) would be half of the diameter = 6 meters.
So, let's plug in the values to the formula and solve for the height (h):
715.92 = 2 * 3.14 * 6² + 2 * 3.14 * 6h
715.92 = 226.08 + 37.68h
489.84 = 37.68h
h = 489.84 / 37.68
h = 13 meters
Therefore, the height of the rectangle is 13 meters.
Use the image to answer the question.
An illustration shows a cylinder with radius, 4.5 inches, and perpendicular height, 12 inches. The cylinder is placed horizontally and the edges that are not visible are represented by a dashed line.
What is the surface area of the cylinder?
(1 point)
Responses
94.5π in.2
94.5 pi in. squared
126π in.2
126 pi in. squared
148.5π in.2
148.5 pi in. squared
108π in.2
108 pi in. squared
The surface area of a cylinder is calculated using the formula:
Surface Area = 2πr² + 2πrh
In this case, the radius (r) is 4.5 inches and the perpendicular height (h) is 12 inches.
Let's plug the values into the formula:
Surface Area = 2 * π * 4.5² + 2 * π * 4.5 * 12
Surface Area = 2 * π * 20.25 + 2 * π * 54
Surface Area = 40.5π + 108π
Surface Area = 148.5π in.²
Therefore, the surface area of the cylinder is 148.5π square inches.
The closest response option is: 148.5π in.²
Which of the following cylinders has the largest surface area?(1 point)
Responses
a cylinder with a radius of 9 in. and a height of 4 in.
a cylinder with a radius of 9 in. and a height of 4 in.
a cylinder with a radius of 6 in. and a height of 12 in.
a cylinder with a radius of 6 in. and a height of 12 in.
a cylinder with a radius of 10 in. and a height of 5 in.
a cylinder with a radius of 10 in. and a height of 5 in.
a cylinder with a radius of 9 in. and a height of 9 in.
To determine which cylinder has the largest surface area, we need to calculate the surface area of each cylinder using the formula:
Surface Area = 2πr² + 2πrh
Let's calculate the surface area of each cylinder based on the given dimensions:
1. Cylinder with a radius of 9 in. and a height of 4 in.
Surface Area = 2π(9)² + 2π(9)(4)
Surface Area = 2π(81) + 2π(36)
Surface Area = 162π + 72π
Surface Area = 234π square inches
2. Cylinder with a radius of 6 in. and a height of 12 in.
Surface Area = 2π(6)² + 2π(6)(12)
Surface Area = 2π(36) + 2π(72)
Surface Area = 72π + 144π
Surface Area = 216π square inches
3. Cylinder with a radius of 10 in. and a height of 5 in.
Surface Area = 2π(10)² + 2π(10)(5)
Surface Area = 2π(100) + 2π(50)
Surface Area = 200π + 100π
Surface Area = 300π square inches
4. Cylinder with a radius of 9 in. and a height of 9 in.
Surface Area = 2π(9)² + 2π(9)(9)
Surface Area = 2π(81) + 2π(81)
Surface Area = 162π + 162π
Surface Area = 324π square inches
Therefore, out of the given options, the cylinder with a radius of 9 in. and a height of 9 in. has the largest surface area with 324π square inches.
A cylinder has a surface area of 312π ft.2. If its height is 20 ft., what is the measure of its radius?(1 point)
Responses
6 ft.
6 ft.
5.5 ft.
5.5 ft.
6.5 ft.
6.5 ft.
5 ft.
The surface area of a cylinder is given by the formula:
Surface Area = 2πr² + 2πrh
Given that the surface area is 312π ft² and the height is 20 ft, we can substitute these values into the formula and solve for the radius (r):
312π = 2πr² + 2πr(20)
312 = 2r² + 40r
2r² + 40r - 312 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring gives:
2(r - 6)(r + 26) = 0
Therefore, the possible solutions are r = 6 ft or r = -26 ft. Since the radius of a cylinder cannot be negative, the radius of the cylinder in this case is 6 ft.
Therefore, the measure of its radius is 6 ft.