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iVinArrow [24]
3 years ago
15

What is the maximum number of cubes with side lengths of 1/2 cm that can fit into a right rectangular prism with base dimensions

of 12 1/2 cm by 8 1/2 cm and height of 9 1/2 cm?
Mathematics
1 answer:
tamaranim1 [39]3 years ago
8 0

Answer:

2,018

Step-by-step explanation:

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Find the area of the shaded region. Round to the nearest hundredth where necessary (2 decimal places
suter [353]

Answer:

117 in²

<u>Finding the area of the trapezoid:</u>

First, we need to find the area of the trapezoid formed by the dotted lines. The formula for finding the area of the trapezoid is "(a₁ + a₂)h/2".

[Where, a₁ = shorter parallel side; a₂ = longer parallel side]

⇒ (a₁ + a₂)h/2 = Area of trapezoid

⇒ (14 + 26)15/2 = Area of trapezoid

⇒ Area of trapezoid = (40)15/2 = (20)15 = 300 in²

<u>Reviewing on how to find the area of the unshaded region:</u>

To find the area of the shaded region, we need to subtract the area of the unshaded region from the area of the trapezoid. In this case, the unshaded region is a triangle whose base is 26 inches. To find the area of the triangle, we need to use the formula 1/2 x Base x Height. We are given the base, but the height is unknown.

<u>Determining the height:</u>

We are given a small side length "6 inches" and the height of the trapezoid "15 inches". If we subtract the small side length from the height of the trapezoid, we will obtain the height of the triangle.

⇒ Height of trapezoid - Small side length = Height of triangle

⇒ 15 - 6 = Height of triangle

⇒ 9 in = Height of triangle

<u>Determining the area of the unshaded region:</u>

Now, let's substitute the base and the height in the formula to find the area of the triangle

⇒ 1/2 x Base x Height

⇒ 1/2 x 26 x 9

⇒ 13 x 9

⇒ 117 in²

<u>Determining the area of the shaded region:</u>

Finally, let's subtract the area of the unshaded region from the area of the trapezoid to obtain the area of the shaded region.

⇒ Area of trapezoid - Area of unshaded region = Area of shaded region

⇒ 300 - 117 = Area of shaded region

⇒ 183 in² = Area of shaded region

5 0
2 years ago
Ten percent of 640 is what number?
Lelechka [254]

Ten percent of 640 is 64.

640/100=6.4

6.4*10=64.

There are many other ways to find this but that is the way I have always used :)

Hope this helps!

4 0
3 years ago
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If Damon goes from his office on the 10th floor to a meeting
solniwko [45]

Answer:

5 and down

Step-by-step explanation:

3 0
3 years ago
What value of n makes the equation true? Show your work.
3241004551 [841]

Answer:

5n

Step-by-step explanation:

(7^5 * 7^n) ^ 4   = (7^11/7^n)^3

7^(20 + 4n)   =  4.7^15 / n^3

= 20/4 = 5n   and  15/3 = 5n

Answer 5n

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Answer:

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Step-by-step explanation:

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