Name the postulate or theorem you can use to prove the triangles congruent.

Mathematics

2 answers:

marissa [1.9K]3 years ago

8 0

Answer: HL Theorem

Step-by-step explanation:

In the given picture, there are two right triangles .

Here one side of both triangles are equal.

Also they both have one side as common.

So they are congruent by HL Theorem.

<em>HL theorem or hypotenuse leg theorem tells that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.</em>

Airida [17]3 years ago

3 0

You have two right triangles that have a corresponding congruent leg and a common hypotenuse, so you can use HL Theorem to prove the triangles congruent.

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Volume: $\frac{2}{3}\pi r^3$

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First of all, we need to find the volume of the hemispherical tank.

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where

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Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:

$V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3$

Now we want to find the ratio between the volume of the hemisphere and its surface area.

The surface area of a sphere is

$A=4 \pi r^2$

For a hemisphere, the area of the curved part of the surface is therefore half of this value, so $2\pi r^2$ . Moreover, we have to add the surface of the base, which is $\pi r^2$ . So the total surface area of the hemispherical tank is