Two answers:
Choice B) area of cylinder base is (1/4)(3.14)x^2
Choice E) height is 4x
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Step-by-step explanation:
The area of a circle is pi*r^2 with r as the radius. The diameter given is x, so half of this is x/2 which is the radius. So r = x/2
The area of the base is
pi*r^2 = pi*(x/2)^2 = pi*(x^2)/4 = (1/4)pi*x^2 = (1/4)(3.14)x^2
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Use this with the volume to find the height
volume of cylinder = (area of base)*(height)
V = (pi*r^2)*h
V = (1/4)(3.14)x^2*h
3.14x^3 = (1/4)(3.14)x^2*h
x^3 = (1/4)x^2*h ....... divide both sides by 3.14
x = 1/4*h .... divide both sides by x^2
4x = h ..... multiply both sides by 4
h = 4x
The height is 4 times the diameter.
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Side notes:
- Choice A is false because x/2 is the actual radius.
- Choice C is similar to B, but the 1/2 should be 1/4.
- Choice D is false as above we found h = 4x. It's likely this is a trick answer if you forget to square x/2 properly.
All of these facts allow us to cross these answer choices off the list.