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What is the surface area of a right rectangular cylinder with a radius
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05 Dec 2022, 02:06
05 Dec 2022, 02:06
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Question Stats:
70% (01:35) correct
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What is the surface area of a right rectangular cylinder with a radius of r and a height that is 1.5 times its diameter?
A. \(6 \pi r^2+4 \pi r\)
B. \(7 \pi r^2\)
C. \(8 \pi r^2\)
D. \(3 \pi r^3 + 2 \pi r^2\)
E. \(3 \pi r^3 + 4 \pi r\)
A. \(6 \pi r^2+4 \pi r\)
B. \(7 \pi r^2\)
C. \(8 \pi r^2\)
D. \(3 \pi r^3 + 2 \pi r^2\)
E. \(3 \pi r^3 + 4 \pi r\)
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Re: What is the surface area of a right rectangular cylinder with a radius
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07 Dec 2022, 07:44
07 Dec 2022, 07:44
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Expert Reply
r=r, d=2r, h=3r
The area of the top of the cylinder is pi(r^2).
The area of the bottom of the cylinder is the same as the top = pi(r^2).
The area of the vertical edge of the cylinder is circumference * height = pi(2r) * 3r = 6pi(r^2).
Adding that all together, we get 8pi(r^2).
Answer: C
The area of the top of the cylinder is pi(r^2).
The area of the bottom of the cylinder is the same as the top = pi(r^2).
The area of the vertical edge of the cylinder is circumference * height = pi(2r) * 3r = 6pi(r^2).
Adding that all together, we get 8pi(r^2).
Answer: C
Re: What is the surface area of a right rectangular cylinder with a radius
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09 Dec 2022, 03:00
09 Dec 2022, 03:00
Expert Reply
OE
C It’s a geometry problem with variables in the answer choices, so draw the figure and set up your scratch paper to Plug In. Plug in an easy number like r = 5; label the radius 5 and the height 15, which is 1.5 times your diameter of 10. The surface area of a cylinder is made up of 3 smaller areas: 2 identical circular bases on top and bottom, and a rectangle that’s the height of the cylinder on one side and the circumference of the base on the other. If r = 5, then the area of each base is 25π, or 50π for the 2 of them. The rectangle is 15 × 10π = 150π, so the total surface area is 200π, your target answer. Plug 5 in for r in the answers, and only choice (C) matches your target answer of 200π.
C It’s a geometry problem with variables in the answer choices, so draw the figure and set up your scratch paper to Plug In. Plug in an easy number like r = 5; label the radius 5 and the height 15, which is 1.5 times your diameter of 10. The surface area of a cylinder is made up of 3 smaller areas: 2 identical circular bases on top and bottom, and a rectangle that’s the height of the cylinder on one side and the circumference of the base on the other. If r = 5, then the area of each base is 25π, or 50π for the 2 of them. The rectangle is 15 × 10π = 150π, so the total surface area is 200π, your target answer. Plug 5 in for r in the answers, and only choice (C) matches your target answer of 200π.
