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olasank [31]
2 years ago
14

How many rectangular prisms 8 inches long, 5 inches wide, and 2 inches high can fit into another rectangular prism that measures

16 inches long, 10 inches wide, and 10 inches high?
Mathematics
1 answer:
tangare [24]2 years ago
8 0

Answer:

20

Step-by-step explanation:

Volume of rectangular prism = length × width × height

Length = 8 inches

Width = 5 inches

Height = 2 inches

Volume of rectanglular prism = length × width × height

= 8 inches * 5 inches * 2 inches

= 80 inches ³

Dimensions of another rectangular prism:

Length = 16 inches

Width = 10 inches

Height = 10 inches

Volume of rectangular prism B = length × width × height

= 16 inches * 10 inches * 10 inches

= 1,600 inches ³

Number of prism A that fits into prism B = Volume of prism B ÷ volume of prism A

= 1,600 inches ³ ÷ 80 inches ³

= 20

Number of prism A that fits into prism B = 20

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Please help with #5 and #8! I don’t really know all of the info to find the volume! (Composite Figures)
bagirrra123 [75]
It looks like you're doing good with breaking-down the composite into digestible pieces. So, don't stress too much!

Keep in mind that the area for a 3D shape is Bh, where "B" is the area of a face & "h" is the height.

#5
Shape A is 3X4X9.
First, calculate the area of a face:

9X4= 36

Multiply by height:

36X3= 108

The process is the same with shape B.
3X4X8
Calculate area of face:

8X4= 32

Multiply by height:

32X3= 96

Now you add both areas:

108+96= 204 cubic feet

I think you're doing pretty good, just don't over think things too much. Try #8 with the similar process seen here. Just comment if you get stuck.

Hope this helps!
6 0
3 years ago
A shipping company is loading cube shaped crates into a larger cube shaped container the smaller cubes have side lengths 21/2 fe
zheka24 [161]

Answer:

64 crates

Step-by-step explanation:

Smaller Cube Side Length = 2 1/2 feet, or, 2.5 feet

Larger Container (Cube) Side Length = 10 feet

We find volume of larger container and find volume of small crates. We divide the large volume by volume of each crate. This will give us number of crates we can fit.

Volume of Cube = x^3

Where x is the side length of the cube

Now,

Small Crate Volume = (2.5)^3 = 15.625 cubic feet

Large Container Volume = 10^3 = 1000 cubic feet

Number of crates that would fit = 1000/15.625 = 64

So, 64 crates will fit in the largest shipping container

7 0
3 years ago
determine which postulate or theorem can be used to prove that abc is congruent to dcb is it sas, aas, sss, or asa?
Zigmanuir [339]
Is there a pic I can use to help?
4 0
3 years ago
Read 2 more answers
What is 7 1/5 - 6 2/5 =?
poizon [28]

Answer:

0.8

Step-by-step explanation:

7 1/5 - 6 2/5 = 0.8

5 0
3 years ago
The base of a pentagonal prism is regular with an apothem of 4 cm. The height of the prism is 16 cm. Find the volume of the pris
Georgia [21]

Answer:

volume ≈ 930 cm³ (nearest cubic cm)

Step-by-step explanation:

The base of the prism which is a pentagon is regular. The apothem which is a line drawn from the center to any side of the pentagon is 4 cm. The height of the prism is 16 cm.

The volume of a prism = Bh

where

B = base area

h = height of the prism

The base of the prism can be divided into 5 congruent triangles.But the base of the triangles is unknown.

The sum of interior angle of a pentagon is 540°. That means each angle is 108° . The triangle divide the angle into 2. Making the 2 base angle as 54° each. The last angle of the triangle at the center is 72°(remember sum of angle in a triangle is 180° which is 54° + 54° + 72° = 180°) .

The angle form the center can be divided by the line of height of the triangles. The angle will then be 36°. Using tangential ratio half of the length of the base of the triangle can be known. Therefore,

tan 36° = opposite/adjacent

tan 36° = opposite/4

opposite = 4 tan 36°

The full base of the triangles = 2(4 tan 36°)

area of each triangle = 1/2 × 2(4 tan 36°) × 4 = 16 tan 36°

Base area of the prism(pentagon) = 5 × 16 tan 36° = 80 tan 36°

Volume of the prism = Bh

where

h = 16 cm

B = 80 tan 36°

volume =  80 tan 36° × 16 = 1280  tan 36° = 1280  × 0.726542528

volume = 929.974435847  cm³

volume ≈ 930 cm³ (nearest cubic cm)

5 0
3 years ago
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