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beks73 [17]
3 years ago
8

One cube has an edge length 5 cm shorter than the edge length of the second cube. The volume of the smaller cube is 216 cm?. Wha

t is the volume of the
larger cube?
Mathematics
1 answer:
VLD [36.1K]3 years ago
4 0

Answer:

The volume of the  larger cube is V=1,331\ cm^3

Step-by-step explanation:

Let

x ---> the length of the smaller cube

y ---> the length of the larger cube

we know that

the volume of a cube is equal to

V=b^3

where

b is the length side of the cube

we have

x=y-5 ----> equation A

The volume of the smaller cube is 216 cm^3

so

substitute in the formula of volume

216=x^3

solve for x

x=\sqrt[3]{216}\ cm

x=6\ cm

<em>Find the value of y</em>

x=y-5

6=y-5

y=6+5=11\ cm

<em>Find the volume of the larger cube</em>

V=y^3

substitute the value of y

V=11^3

V=1,331\ cm^3

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Hi, I'm happy to help!

To solve this, we need to find the distance from the origin to the y coordinate value, x coordinate value, then use the Pythagorean Theorem.

The origin of a graph (center) has the coordinates (0,0), so this will be our other coordinates.

First, let's find the x coordinate distance change. We move from the x coordinate 0, to the x coordinate -8, <u>so we move 8 x units.</u>

Next, let's find the y coordinate distance change. We move from the y coordinate 0, to the y coordinate 4, <u>so we move 4 y units.</u>

Now that we have these two leg lengths, let's imagine this as a right triangle. Moving from the origin, we draw a line from (0,0), to (-8,0). Then, we draw a line from (-8,0) to (-8,4). Now, draw a direct line from (0,0), to (-8,4). We have the length of the first(8) and second(4) lines, and we need to find the third line length to find our answer. To do this, we use the Pythagorean Theorem, which states that a²+b²=c². This says that, in a right triangle, the square of the two shorter lengths equals the square of the longest length. The longest length is what we are solving for.

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<u>To summarize the distance between the origin and the coordinates (-8,4), is about 8.9.</u>

I hope this was helpful, keep learning! :D

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