Mathematics, 10.04.2020 18:40, priarm8799

How many cubes with side lengths of 1/4cm does it take to fill the prism?
Length: 2cm
Width: 7/4cm
Height: 1cm

How many cubes with side lengths of 1/4cm does it take to fill the prism? Length: 2cm Width: 7/4cm H

Answers: 1

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answered: aleanroverto723

Given:

The length of the rectangular prism is 2 cm.

The width of the prism is $\frac{7}{4}$ cm.

The height of the prism is 1 cm.

The side lengths of the cube is $\frac{1}{4}$ cm.

We need to determine the number of cubes with side lengths $\frac{1}{4}$ would fill the prism.

Volume of the cube:

The volume of the cube can be determined using the formula,

V=s^3

Substituting the value, we get;

$V=(\frac{1}{4})^3$

$V=\frac{1}{64}$

Thus, the volume of the cube is $\frac{1}{64} \ cm^3$

Volume of the rectangular prism:

Volume of the rectangular prism can be determined using the formula,

V=lwh

Substituting the values, we get;

$V=2\times \frac{7}{4} \times 1$

$V=3.5 \ cm^3$

Thus, the volume of the rectangular prism is 3.5 cm³

Number of cubes:

The number of cubes can be determined by dividing the volume of the prism by the volume of the cube.

Thus, we have;

$No. \ of \ cubes=\frac{3.5}{\frac{1}{64}}$

$No. \ of \ cubes=3.5 \times 64$

$No. \ of \ cubes=224$

Thus, the number of cubes that fill the prism are 224 cubes.

answered: Guest

me! what did you put for this question?

step-by-step explanation:

answered: Guest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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How many cubes with side lengths of 1/4cm does it take to fill the prism?
Length: 2cm
Wi...