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2 years ago

18

Mathematics

1 answer:

Alla [95]2 years ago

6 0

Answer:

40x30= 1200, 20x15=300, 300/1200= 1/4.

Step-by-step explanation:

You can also visualize it. Imagine a field 40’ long and the boy cut the top 20’ of it but left 20’ of the bottom, he would have cut half of it at this point. Now it’s 30’ wide and he cut the left 15’ of what’s remaining but left the right 15’ uncut. So now there’s a 20’x15’ bottom right corner left uncut. There are 4 sections that are 20’x15’ and he left one out of four uncut, otherwise written as 1/4.

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A. figure ABCD is similar to figure A'B'C'D'

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2 years ago

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Pls help

KATRIN_1 [288]

Answer:

169.04 in² (nearest hundredth)

Step-by-step explanation:

Surface area of a cone = $\pi$ r² + $\pi$ r $l$

(where r = radius of the base and $l$ = slant height)

Given slant height $l$ = 10 and surface area = 188.5

Surface area = $\pi$ r² + $\pi$ r $l$

188.5 = $\pi$ r² + 10 $\pi$ r

$\pi$ r² + 10 $\pi$ r - 188.5 = 0

r = $\frac{-10\pi +\sqrt{(10\pi )^2-(4\times\pi \times-188.5)} }{2\pi }$ = 4.219621117...

Volume of a cone = (1/3) $\pi$ r²h

(where r = radius of the base and h = height)

We need to find an expression for h in terms of $l$ using Pythagoras' Theorem a² + b² = c², where a = radius, b = height and c = slant height

r² + h² = $l$ ²

h² = $l$ ² - r²

h = √( $l$ ² - r²)

Therefore, substituting found expression for h:

volume of a cone = (1/3) $\pi$ r²√( $l$ ² - r²)

Given slant height $l$ = 10 and r = 4.219621117...

volume = 169.0431969... = 169.04 in² (nearest hundredth)

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2 years ago

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Identify the volume of the composite figure, rounded to the nearest tenth. PLEASE HELP!!!

Anni [7]

Answer:

The volume of the composite figure is:

312 ft^3

Step-by-step explanation:

To identify the volume of the composite figure, you can divide it in the known figures there, in this case, you can divide the figure in a cube and a pyramid with a square base. Now, we find the volume of each figure and finally add the two volumes.

VOLUME OF THE CUBE.

Finding the volume of a cube is actually simple, you only must follow the next formula:

Volume of a cube = base * height * width

So:

Volume of a cube = 6 ft * 6 ft * 6 ft
Volume of a cube = 216 ft^3

VOLUME OF THE PYRAMID.

The volume of a pyramid with a square base is:

Volume of a pyramid = 1/3 B * h

Where:

B = area of the base.

h = height.

How you can remember, the area of a square is base * height, so B = 6 ft * 6 ft = 36 ft^2, now we can replace in the formula:

Volume of a pyramid = 1/3 36 ft^2 * 8 ft
Volume of a pyramid = 96 ft^3

Finally, we add the volumes found:

Volume of the composite figure = 216 ft^3 + 96 ft^3
Volume of the composite figure = 312 ft^3

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2 years ago