A sphere with a radius of 6cm has the same volume as a cylinder with a height of 4.5cm. What is the radius of the cylinder

1 answer:

4 0

Short answer: r = 8
Remark
The easiest way to do this is to solve the sphere's volume in terms of pi. When you do this, you can equate that to the formula for a cylinder and cancel the pi values.

Step One
Find the volume of the sphere.

Givens
r = 6 cm

Formula
V = (4/3) pi r^3

Sub and Solve
V = 4/3 pi * 6^3
V = 288 * pi

Step two
Find the radius of the cylinder

Givens
V = 288* pi cm^3
h = 4.5 cm

Formula
V = pi r^h

Sub and solve
288 pi cm^3 = pi r^2 * 4.5 Divide both sides by pi
288 cm^3 = 4.5 r^2 Divide both sides by 4.5
388 / 4.5 = r^2
64 = r^2 Take the square root of both sides.
r = square root( 64)
r = 8 <<<<< Answer

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The table on the left is that of a linear function, and the one on the right is that of an exponential function. Can you tell wh

Brut [27]

The correct answer is D.

As you can see, the exponential function grows by doubling the previous output with each increment of the input: start with 1, you double it to get 2, then you double it to get 4, 8 and so on.

On the other hand, the linear function adds 7 with each step. This means that the exponential function will eventually reach and pass the linear one, and will definitely be grater from that point on. In fact, if we continue the table, we get

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