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Salsk061 [2.6K]
3 years ago
7

A rectangular pyramid has a base with dimensions 5 inches by 7 inches. The height of the pyramid is unknown. If the volume of th

e pyramid is 105 cubic inches, what is the height of the pyramid? Explain the steps
Mathematics
2 answers:
PolarNik [594]3 years ago
8 0

Answer:

Substitute the area of the base and the volume into the formula V = 1

3

Bh. After substituting, you have 105 = 1

3

(35)h. Solve for h by multiplying both sides by 3 and then dividing both sides by 35. The height is 9 inches.

Step-by-step explanation:

Ksenya-84 [330]3 years ago
4 0

Answer:

The height of the pyramid is 9\ in

Step-by-step explanation:

we know that

The volume of the rectangular pyramid is equal to

V=\frac{1}{3}BH

where

B is the area of the rectangular base of the pyramid

H is the height of the pyramid

<u>Find the area of the base B</u>

B=5*7=35\ in^{2}

we have

V=105\ in^{3}

substitute the value of B and the value of V in the formula and solve for H

105=\frac{1}{3}(35)H

315=(35)H

H=315/35=9\ in

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Now, we cancel the common factor y
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Step-by-step explanation:

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Read 2 more answers
The coordinates of each rectangle ABCD are A (0,2) B (2,4) C (3,3) D (1,1). Find the distance of each side of the rectangle then
EastWind [94]

AB = CD = √8 ≈ 2.8 units

BC = AD = √2 ≈ 1.4 units

Area of the rectangle ABCD = 3.92 units²

Perimeter of the rectangle ABCD = 8.4 units

<h3>How to Find the Area and Perimeter of a Rectangle?</h3>

Given the coordinates of vertices of rectangle ABCD as:

  • A(0,2)
  • B(2,4)
  • C(3,3)
  • D(1,1)

To find the area and perimeter, use the distance formula to find the distance between A and B, and B and C.

Using the distance formula, we have the following:

AB = √[(2−0)² + (4−2)²]

AB = √[(2)² + (2)²]

AB = √8 ≈ 2.8 units

CD = √8 ≈ 2.8 units

BC = √[(2−3)² + (4−3)²]

BC = √[(−1)² + (1)²]

BC = √2 ≈ 1.4 units

AD = √2 ≈ 1.4 units

Area of the rectangle ABCD = (AB)(BC) = (2.8)(1.4) = 3.92 units²

Perimeter of the rectangle ABCD = 2(AB + BC) = 2(2.8 + 1.4) = 8.4 units

Learn more about the area and perimeter of rectangle on:

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