Answer: 1560 cubic centimeters
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Step-by-step explanation:
Break the 3D figure into two pieces:
- A cylinder on top.
- A cone on the bottom.
The relevant formulas we need are:
- V = pi*r^2*h = volume of a cylinder
- V = (1/3)*pi*r^2*h = volume of a cone
where r and h are the radius and height respectively.
The cylinder has radius r = 5 and height h = 17.8
V = pi*r^2*h
V = pi*5^2*17.8
V = 445pi
The cone has the same radius, but the height is h = 24-17.8 = 6.2
V = (1/3)*pi*r^2*h
V = (1/3)*pi*5^2*6.2
V = (155/3)pi
The total volume is then,
445pi+(155/3)pi
(1335/3)pi + (155/3)pi
(1335/3 + 155/3)pi
(1490/3)pi
That's the exact volume of this pencil-shaped figure. This exact volume is in terms of pi.
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Now to compute the approximate volume.
If you were to use pi = 3.14, then the approximate volume is
(1490/3)pi = (1490/3)*3.14 = 1559.5333 cubic cm
Here's what my calculator shows when computing the expression.
(1490/3)pi = 1560.32435128293
The calculator has a stored version of pi with more digits for better accuracy.
Both of those results round to 1560 cubic cm when rounding to the nearest cubic centimeter.