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kozerog [31]
3 years ago
10

Find the volume of the square pyramid below

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
7 0

Answer:

A

Step-by-step explanation:

The volume (V) of a pyramid is

V = \frac{1}{3} area of base × perpendicular height (h)

area of square base = 4² = 16 and h = 4, hence

V = \frac{1}{3} × 16 × 4 = \frac{64}{3} = 21 \frac{1}{3} ft³

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Here is a diagram of a black circle inside a white square and a diagram of a small grey square inside a white square.
nika2105 [10]

The ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2

<h3>How to determine the ratio of the areas?</h3>

The side length AB is given as:

AB = 8x

The area of the white square is calculated as

White = (AB)²

This gives

White = (8x)²

Evaluate

White = 64x²

The side length AB represents the diameter of the black circle.

So, the radius is:

r =AB/2

This gives

r = 8x/2 = 4x

The area is then calculated as:

Circle = πr²

This gives

Circle = π(4x)²

Evaluate

Circle = 16πx²

Next, calculate AW and AZ using:

AZ = AW = AB/2

Evaluate

AZ = AW = 8x/2 = 4x

Calculate WZ using the following Pythagoras theorem

WZ² = AW² + AZ²

This gives

WZ² = (4x)² + (4x)²

Evaluate

WZ² = 2(4x)²

Take the square root of both sides

WZ = 4x√2

The area of the gray square is:

Gray = WZ²

This gives

Gray = 2(4x)²

Evaluate

Gray = 32x²

At this point, the areas are:

  • White = 64x²
  • Circle = 16πx²
  • Gray = 32x²

The ratio is then represented as:

Ratio = Circle : White : Gray

This gives

Ratio = 16πx² : 64x² : 32x²

Divide through by 16x²

Ratio = π : 4 : 2

Hence, the ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2

Read more about areas at:

brainly.com/question/24487155

#SPJ1

6 0
2 years ago
What is the 70th term of the sequence that begins -3,1,5,9?
VashaNatasha [74]
The 70th term is 277
Hope this helps
3 0
3 years ago
How many solutions does the following<br> equation have?<br> 7(y + 3) = 5y + 8<br><br> answer:
vodomira [7]

Answer:

One Solution

Explanation:

7(y + 3) = 5y + 8

Simplify both sides of the equation

7(y + 3) = 5y + 8

(7)(y) + (7)(3) = 5y + 8 (Distribute)

7y + 21 = 5y + 8

Subtract 5y from both sides

7y + 21 − 5y = 5y + 8 − 5y

2y + 21 = 8

Subtract 21 from both sides

2y + 21 − 21 = 8 − 21

2y = −13

Divide both sides by 2

2y = −13

2y / 2 = -13 / 2

y = -13 / 2

-13 / 2 = -6.5

y = -13 / 2 or -6.5

6 0
3 years ago
Round 5,382,619 to the nearest 10,000
Radda [10]
The answer is 5,380,000
4 0
3 years ago
Read 2 more answers
What is the answer to the question?
IrinaVladis [17]

Answer:

the answer is option 4th

3 0
3 years ago
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