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Umnica [9.8K]
3 years ago
11

A rectangular box has interior dimensions 6-inches by 5-inches by 10-inches. The box is filled with as many solid 3-inch cubes a

s possible, with all of the cubes entirely inside the rectangular box. What percent of the volume of the box is taken up by the cubes?
Mathematics
1 answer:
Arte-miy333 [17]3 years ago
8 0

Answer: The box would have 99% of its volume taken up.

Step-by-step explanation: The box has dimensions as follows;

Length = 6 inches

Width = 5 inches

Height = 10 inches

Therefore the volume of the box shall become

Volume = L x W x H

Volume = 6 x 5 x 10

Volume = 300 cubic inches

Also a 3 inch cube would have its volume given as follows (

Volume = 3 x 3 x 3 (All sides of a cube has equal lengths)

Volume = 27 cubic inches

To find out how many of 3-inch cubes can fit in, divide 300 by 27 and that equals 11.11.

Hence you can have at most 11 cubes in the box. The total volume of 11 cubes is given as 11 x 27 which equals 297. Therefore, the percentage of the box taken up completely by the cubes is given as;

Percentage = (Volume of cubes/Volume of box) x 100

Percentage = (297/300) x 100

Percentage = 99

Therefore the box would have 99% of its volume taken up by the cubes.

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vfiekz [6]

Answer:

its the 3rd choice.

Step-by-step explanation:

Firstly, we find angle BDC (180-90-30=60)

Now that we found it we can use the sine rule to find DB (which i put as an x), which is sin60/14=sin30/x, by cross multiplication, we find that its equal to a decimal number, i will use its root version to this easier, its equal to 14sqrt3/3 inches.

And now we use the pythagorean theorem to find DC, we find that it is equal to 28sqrt3/3

Now, we find angle BAC (180-90-(30+15)=45)

Again, we use the sine rule to find AB (whom i will refer to as x and from whom we will subtract DB to find the length of AD), so we cross multiply in sin45/14=sin(30+15)/x, it is equal to 14.

So since AB-DC=AD

14-(14sqrt3/3)= 5.917096231 (and we ound that to a 5.9)

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3 years ago
The radius of a circle is 10 meters. What is the area of a sector bounded by a 90 degree arc?Give the exact answer in simplest f
Wittaler [7]

Since we know a circle has 360 degrees, the sector bounded by a 90 degree arc will be a quarter of circle (360/90 = 4). Then, to calculate the area of that sector, we can calculate the total area of the circle of radius 10, and then divide it by 4.

The area of a cirlce of radius r is:

A=\pi r^2

Then, the area of the sector would be:

A_s=\frac{\pi r^2}{4}A_s=\frac{\pi(10m)^2}{4}=\frac{100\pi}{4}m^2A_s=25\pi m^2

4 0
1 year ago
Simplify: (- sqrt x-4)^2<br> -X + 4<br> X-4<br> 2x - 8
kaheart [24]

Answer:x-4

Step-by-step explanation:because (-1)x(-1)=1

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3 years ago
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baherus [9]

Answer:

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A population mean of 360, a standard deviation of 4, and a margin of error of 2.5%
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Answer:

(351.04, 368.96)

Step-by-step explanation:

Given that population mean= 360

Std devitaion = 4

margin of error = 2.5%= 0.025

Since population std deviation is known we can use Z critical value

For two tailed critical value for 2.5% would be

2.24

Margin of error = ±Critical value*std deviation

= ±2.24(4)

= ±8.96

Confidence interval =(Mean - margin of error, mean + margin of error)

=(360-8.96, 360+8,.96)\\= (351.04, 368.96)

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4 years ago
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