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3 years ago

What is the volume of this square pyramid? Enter your answer in the box.

Mathematics

2 answers:

musickatia [10]3 years ago

6 0

Answer:400. 10^2 x 12/3 = 400.

katovenus [111]3 years ago

3 0

Answer:

The volume of the given square pyramid is $400m^3$ .

Step-by-step explanation:

From the figure, it is given that the base side of the given square pyramid is=10 m and the height of the square pyramid is=12m, then

The volume of the square pyramid is $V=\frac{1}{3}a^2h$

⇒ $V=\frac{1}{3}(10)^2(12)$

⇒ $V=100{\times}4$

⇒ $V=400m^3$

Thus, the volume of the given square pyramid is $400m^3$ .

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If you can solve all parts I will give brainliest (also give strategy)

Alexxx [7]

The Halloween conical hat, with given height, circular base and brim

extension has the following calculated parameters;

Part a. The slant height is 18.2 inches

Part b. The volume of the cone is $37\frac{1}{2} \cdot \pi$ in.³

Part c. The area of the brim, A = 36·π in.²

Part d. The area of the brim is found by subtracting the area of the base of the cone from the area covered by the perimeter of the brim

Reasons:

Known parameters;

Height of the conical portion, h = 18 inches

Base circumference, C = 5·π inches

Part a. Slant height of the conical portion; Required

Solution:

The circumference of a circle, C = 2·π·r

Therefore;

$r = \dfrac{C}{2 \cdot \pi}$

Which gives;

$r = \dfrac{5 \cdot \pi}{2 \cdot \pi} = \dfrac{5}{2} = 2.5$

Radius, r = 2.5 inches

According to Pythagoras's theorem, we have; s² = r² + h²

Where;

s = The slant height of the cone

s² = 2.5² + 18² = 330.25

s = √(330.25) ≈ 18.2

The slant height, s ≈ 18.2 inches

Part b. The measure in cubic inches of candy that exactly fills the conical portion of the hat is the volume of the cone.

$Volume \ of \ a \ cone = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h$

Therefore;

$V = \dfrac{1}{3} \times \pi \times 2.5^2 \times 18 = 37\frac{1}{2} \cdot \pi$

The volume of the cone, V = $37\frac{1}{2}$ ·π in.³

Part c. The extension of the brim from the base of the cone = 4 inches

The radius of the brim, R = Radius of the base of the cone + 4 inches

∴ R = 2.5 inches + 4 inches = 6.5 inches

Area of the brim, A = Area of the 6.5 inch circle - Area of the circular base of the cone

∴ A = π × 6.5² - π × 2.5² = 36·π

The area of the brim, A = 36·π in.²

Part d. The procedure for solving the question in part c, is described as follows;

The area of the brim can be found by finding the entire area of the circle formed by the perimeter of the brim, then subtracting the area of the base of the cone from that area.

Learn more here:

brainly.com/question/17023854

4 0

3 years ago

Math SAT: Suppose the national mean SAT score in mathematics was 510. In a random sample of 50 graduates from Stevens High, the

sukhopar [10]

Answer:

Mean SAT score for Stevens High graduates are not the same as the national average.

Step-by-step explanation:

We are given the following information in question:

Population mean, μ = 510

Sample mean, $\bar{x}$ = 501

Sample size, n = 50

Alpha, α = 0.10

Sample standard deviation, s = 30

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 510\\H_A: \mu \neq 510$

We use Two-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n-1}} }$ Putting all the values, we have,

$t_{stat} = \displaystyle\frac{501 - 510}{\frac{30}{\sqrt{49}} } = -2.1$ Now,

$t_{critical} \text{ at 0.10 level of significance, 49 degree of freedom } = \pm 1.6765$ Since,

$t_{stat} < t_{critical}$

We reject the null hypothesis and fail to accept it.

We accept the alternate hypothesis and mean SAT score for Stevens High graduates are not the same as the national average.

3 0

3 years ago

The football team plays at a stadium with

12345 [234]

Answer:

1,100

Step-by-step explanation:

6 0

2 years ago

In a recipe mike uses 4 cups of brown sugar for every 3 cups of flower. What is ratio of flour to brown sugar SIMPLEST FORM.

kicyunya [14]

Answer:

3:12 = 1:4

Step-by-step explanation:

3 cups of flour = 4 cups brown sugar

4 x 3 = 12

3:12 = 1:4 (simplest form)

5 0

2 years ago

1.What are the zeros of the polynomial function?

Lorico [155]

Let's to the first example:

f(x) = x^2 + 9x + 20

Ussing the formula of basckara

a = 1
b = 9
c = 20

Delta = b^2 - 4ac

Delta = 9^2 - 4.(1).(20)

Delta = 81 - 80

Delta = 1

x = [ -b +/- √(Delta) ]/2a

Replacing the data:

x = [ -9 +/- √1 ]/2

x' = (-9 -1)/2 <=> - 5

Or

x" = (-9+1)/2 <=> - 4
_______________

Already the second example:

f(x) = x^2 -4x -60

Ussing the formula of basckara again

a = 1
b = -4
c = -60

Delta = b^2 -4ac

Delta = (-4)^2 -4.(1).(-60)

Delta = 16 + 240

Delta = 256

Then, following:

x = [ -b +/- √(Delta)]/2a

Replacing the information

x = [ -(-4) +/- √256 ]/2

x = [ 4 +/- 16]/2

x' = (4-16)/2 <=> -6

Or

x" = (4+16)/2 <=> 10
______________

Now we are going to the 3 example

x^2 + 24 = 14x

Isolating 14x , but changing the sinal positive to negative

x^2 - 14x + 24 = 0

Now we can to apply the formula of basckara

a = 1
b = -14
c = 24

Delta = b^2 -4ac

Delta = (-14)^2 -4.(1).(24)

Delta = 196 - 96

Delta = 100

Then we stayed with:

x = [ -b +/- √Delta ]/2a

x = [ -(-14) +/- √100 ]/2

We wiil have two possibilities

x' = ( 14 -10)/2 <=> 2

Or

x" = (14 +10)/2 <=> 12
________________

To the last example will be the same thing.

f(x) = x^2 - x -72

a = 1
b = -1
c = -72

Delta = b^2 -4ac

Delta = (-1)^2 -4(1).(-72)

Delta = 1 + 288

Delta = 289

Then we are going to stay:

x = [ -b +/- √Delta]/2a

x = [ -(-1) +/- √289]/2

x = ( 1 +/- 17)/2

We will have two roots

That's :

x = (1 - 17)/2 <=> -8

Or

x = (1+17)/2 <=> 9

Well, this would be your answers.

7 0

3 years ago