Problem 3
<h3>Answer: 75 cubic inches</h3>
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Explanation:
It doesn't matter what shape the base is, so the fact it's a hexagon isn't useful info here. What is useful is that the area of the base is 25 square inches.
We multiply this base area by the height, and then divide by 3 to get the volume of the pyramid.
V = (BaseArea*height)/3
V = (25*9)/3
V = 75 cubic inches
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Problem 4
<h3>Answer: </h3><h3>Exact volume = 1440pi cubic cm</h3><h3>Approximate volume =
4521.6 cubic cm</h3>
The approximate volume is found by using pi = 3.14
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Explanation:
We apply this formula to find the volume of a cone
V = (1/3)*pi*r^2*h
In this case, r = 12 is the radius (half the diameter) and h = 30 is the height.
So,
V = (1/3)*pi*12^2*30
V = (1/3)*pi*4320
V = (1/3)*4320*pi
V = 1440pi ...................... exact volume in terms of pi
V = 1440*3.14
V = 4521.6 ....................... approximate volume if you use pi = 3.14
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Problem 5
<h3>Answer: 27 times larger volume</h3>
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Explanation:
Mary's cube has side lengths of 5 inches, so the volume of this cube is 5*5*5 = 5^3 = 125 cubic inches.
James then wants to triple the side lengths of her cube to have a new larger cube that has side lengths of 3*5 = 15 inches. The volume of this new larger cube is going to be 15*15*15 = 15^3 = 3375
To compare the two volumes, we'll divide the larger over the smaller
(larger volume)/(smaller volume) = (3375)/(125) = 27
This number 27 is due to cubing the value 3, ie 3^3 = 3*3*3 = 27
So the larger cube is 27 times larger compared to the smaller cube.
As another example, let's say he wanted to only double the side lengths. This would mean the larger volume is 8 times larger, since 2^3 = 2*2*2 = 8. Whatever the linear scale factor is, cube it and you'll get the volume scale factor.
