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The dimensions of two pyramids formed of sand are shown. How much more sand is in the pyramid with greater volume?

100 points on this The dimensions of two pyramids formed of sand are shown How much more sand is in the pyramid with greater volume class=

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PoumonNeedsHelp

Answer: 5 more cubic inches of sand.

Step-by-step explanation:

If the base area is 25 inches^2 and the height is 9 inches, then you can set up the following equation:

25 * 9/3

Solving that would get 75 inches^3 since 25 * 9 is 225 and dividing it by 3 would get 75.

For the other pyramid, it's base area is 30 inches^2 and it's height is 7 inches long so you can set up the same equation with different numbers:

30 * 7/3

That would be 70 inches^3 since 7 * 30 is 210 and dividing it by 3 would get 70.

Now that we have the volume of both pyramids, we can compare:

70 - 75 = 5 more cubic inches of sand

msm555

Answer:

5

Step-by-step explanation:

To calculate the volume of each pyramid, we use the formula:

[tex] \Large\boxed{\boxed{ \textsf{Volume} = \dfrac{1}{3} \times \textsf{Base Area} \times \textsf{Height}}} [/tex]

For the left pyramid:

[tex] \textsf{Volume}_{\textsf{left}} = \dfrac{1}{3} \times 25 \times 9\\\\ = \dfrac{225}{3} \\\\= 75 \, \textsf{in}^3 [/tex]

For the right pyramid:

[tex] \textsf{Volume}_{\textsf{right}} = \dfrac{1}{3} \times 30 \times 7\\\\ = \dfrac{210}{3} \\\\= 70 \, \textsf{in}^3 [/tex]

Now, to find how much more sand is in the pyramid with greater volume, we subtract the volume of the smaller pyramid from the volume of the larger pyramid:

[tex] \textsf{Difference} = \textsf{Volume}_{\textsf{left}} - \textsf{Volume}_{\textsf{right}} [/tex]

[tex] \textsf{Difference} = 75 - 70 [/tex]

[tex] \textsf{Difference} = 5 \, \textsf{in}^3 [/tex]

So, there are [tex]\boxed{5} [/tex] cubic inches more sand in the pyramid with greater volume.

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