the volume of a bucket of water is 864 cubic inches. how many buckets are needed to fill a 7 cubic foot tank?

We have the relation:

1ft = 12 inches.

Then, if we cube both sides, we have:

(1ft)^3 = (12 in)^3

1ft^3 = 288 in^3.

Now we know that:

The bucket is 864 in^3

The tank is 7 ft^3.

knowing that 1 ft^3 = 288in^3

Then 7 ft^3 is seven times that:

7ft^3 = 7*(1ft^3) = 7*(288in^3) = 2016 in^3

Now the number of buckets needed to completely fill the tank is:

N = (2016 in^3)/(864in^3) = 2.33

So you need 2.33 buckets, or we can round it up to 3 buckets, where the third bucket will have some water inside it when the tank is completely filled.

the answer is 1/4

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4