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kaheart [24]
2 years ago
11

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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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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We now calculate the area to obtain,


Area=\frac{1}{2}\times 6\times 4 =3\times 12=12

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