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2 years ago

A right triangle of hypotenuse 13 cm and

Mathematics

1 answer:

wariber [46]2 years ago

8 0

9514 1404 393

Answer:

volume: 100π cm³ ≈ 314.2 cm³
area: 65π cm² ≈ 204.2 cm²

Step-by-step explanation:

The other leg of the right triangle is found from the Pythagorean theorem:

r² + 12² = 13²

r = √(169 -144) = √25 = 5

The solid of revolution is a cone with a radius of 5, a height of 12, and a slant height of 13.

The volume is given by ...

V = (1/3)πr²h

V = (1/3)π(5 cm)²(12 cm) = 100π cm³ . . . volume

The lateral surface area is given by ...

LA = πrh . . . where h is the slant height

LA = π(5 cm)(13 cm) = 65π cm² . . . curved surface area

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Mars2501 [29]

ANSWER

The area of triangle DEF is $12$ square units.

EXPLANATION

The area of triangle DEF can be found using the formula,

$Area=\frac{1}{2}\times base \times height$ .

From the diagram, we can see that the height of the triangle is bounded between $x=-7$ and $x=-11$ .

We use the absolute value method to find the height to be,

$Height=|-7--11|=|-7+11|=|4|=4$ .

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We can again use the absolute value method to to determine the length of the base to be,

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