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kaheart [24]
3 years ago
11

A right triangle of hypotenuse 13 cm and

Mathematics
1 answer:
wariber [46]3 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:

Answer:

a) The base of the rectangular pyramid shown has an area of

60 square inches

b) A triangular face with a base of 10 inches has an area of 28 square inches.

c) A triangular face with a base of 5 inches has an area of 17.75 square inches.

d) The total surface area of the pyramid is 151.5 square inches.

Step-by-step explanation:

a) Solving for question a, we were given the following parameters

A rectangular pyramid. The rectangular base has a length of 10 inches and a width of 6 inches

The formula used to calculate the rectangular base of a rectangular pyramid =

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Where :

Length = 10 inches

Width = 6 inches

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Hence, the base of the rectangular pyramid shown has an area of 60 square inches

b) Solving for question b, we have the following values given:

2 triangular sides have a base of 10 inches and height of 5.6 inches.

First step would be to solve for one triangular side first.

The area of the one triangular side = (Base × Height) ÷ 2

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Therefore, for the 2 triangular sides, since they have the same base and height, the other side as well would be 28 inches².

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c) Solving for question c, the following parameters are given:

2 triangular sides have a base of 5 inches and height of 7.1 inches.

We would be to solving for one triangular side first.

The area of the one triangular side = (Base × Height) ÷ 2

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Therefore, for the 2 triangular sides, since they have the same base and height, the other side as well would be 17.75 inches².

A triangular face with a base of 5 inches has an area of 17.75 square inches.

d) Solving for d, it is important to note that, a rectangular pyramid has 5 faces and they are: The rectangular base and 4 triangular faces

The formula for the total surface area of the rectangular pyramid is given as

Total Surface Area of the rectangular pyramid = Rectangular Base + Area of Triangular Side A + Area of Triangular Side B + Area of Triangular Side C + Area of Triangular Side D + Area of Triangular Side E

Total Surface Area of the Rectangular Pyramid = 60 inches² + 28 inches² + 28 inches² + 17.75 inches² + 17.75 inches²

Total surface Area of the Rectangular pyramid = 151.5 inches²

The total surface area of the pyramid is 151.5 square inches.

Step-by-step explanation:

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