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A cylinder has a volume of 48π cm3 and height h. Complete this table for volume of cylinders with the same radius but different heights.

height (cm) volume (cm3)
h 48π
2h ? answer in pi
5h ? answer in pi
h/2 ? answer in pi
h/5 ? answer in pi

User Sashank
by
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2 Answers

6 votes

Final answer:

To calculate the volume for different heights, the volume formula V = πr²h is used, showing that the volume changes proportionally with height. The completed table includes volumes for heights 2h, 5h, h/2, and h/5.

Step-by-step explanation:

The volume of a cylinder is given by the formula V = πr²h, where r is the radius, h is the height, and π (pi) represents the mathematical constant roughly equal to 3.14159. Given the volume of the cylinder is 48π cm³ for a height h, changing the height will proportionately change the volume. We can complete the table as follows:

For height 2h: Volume = πr²(2h) = 2(πr²h) = 2(48π cm³) = 96π cm³

For height 5h: Volume = πr²(5h) = 5(πr²h) = 5(48π cm³) = 240π cm³

For height h/2: Volume = πr²(h/2) = 1/2(πr²h) = 1/2(48π cm³) = 24π cm³

For height h/5: Volume = πr²(h/5) = 1/5(πr²h) = 1/5(48π cm³) = 9.6π cm³

User Rlbond
by
8.3k points
6 votes

Answer:

(i) For
2\cdot h, the volume is
96\pi cubic centimeters.

(ii) For
5\cdot h, the volume is
240\pi cubic centimeters.

(iii) For
(h)/(2), the volume is
24\pi cubic centimeters.

(iv) For
(h)/(5), the volume is
9.6\pi cubic centimeters.

Step-by-step explanation:

The volume of the cylinder (
V), measured in cubic centimeters, is defined by the following formula:


V = \pi\cdot r^(2)\cdot h (1)

Where:


r - Radius, measured in centimeters.


h - Height, measured in centimeters.

From statement, we understand that volume of the cylinder is directly proportional to its height. That is:


V \propto h


V = k\cdot h (2)

Where
k is the proportionality constant, measured in square centimeters.

In addition, we eliminate this constant by constructing the following relationship:


(V_(2))/(V_(1)) = (h_(2))/(h_(1))


V_(2) = (h_(2))/(h_(1)) \cdot V_(1) (3)

Based on (3) and knowing that
V_(1) = 48\pi, we calculate the volumes for each height ratio:

(i) For
2\cdot h, the volume is
96\pi cubic centimeters.

(ii) For
5\cdot h, the volume is
240\pi cubic centimeters.

(iii) For
(h)/(2), the volume is
24\pi cubic centimeters.

(iv) For
(h)/(5), the volume is
9.6\pi cubic centimeters.

User Tom Kregenbild
by
7.5k points
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