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valentina_108 [34]
3 years ago
13

What is the approximate volume of a cone with a height of 12 in. and radius of 9 in.?

Mathematics
1 answer:
Arisa [49]3 years ago
8 0
Volume of the cone = 1/3π r^2 h
So, we are given that r = 9 and h = 12
plugging in all the known values 
1/3 * (3.14) * 9 * 9 * 12
= 1017.36 cm³
or
≈1017.4 cm³
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The perimeter of a rectangular park is 500 feet. The length of the park is 100 feet longer than the width. Find the length of th
lord [1]

Answer:

The length of the park is 175 feet

Step-by-step explanation:

Let us solve the question

∵ The perimeter of a rectangular park is 500 feet

∵ The formula of the perimeter of the rectangle is P = 2(L + W)

∵ L is the length and W is the width

→ Equate the rule of the perimeter by 500

∴ 2(L + W) = 500

→ Divide both sides by 2

∴ L + W = 250 ⇒ (1)

∵ The length of the park is 100 feet longer than the width

→ That means L is W plus 100

∴ L = W + 100 ⇒ (2)

→ Substitute L in (1) by (2)

∵ W + 100 + W = 250

→ Add the like terms

∵ (W + W) + 100 = 250

∴ 2W + 100 = 250

→ Subtract 100 from both sides

∵ 2W + 100 - 100 = 250 - 100

∴ 2W = 150

→ Divide both sides by 2

∴ W = 75

→ Substitute the value of W in (2) to find L

∵ L = 75 + 100 = 175

∴ The length of the park is 175 feet

6 0
3 years ago
Is the point 3/5 and 4/5 corresponds to an angle in the unit circle what is the csc
Mariulka [41]

<u>Answer:</u>

csc = 5/4

<u>Step-by-step explanation:</u>

Assuming that the two given points 3/5 and 4/5 are the two sides of a triangle and a right angle 0  with legs x and y and z as its hypotenuse.

Then using Pythagoras Theorem:

z^2=x^2+y^2

z^2=(\frac{3}{5} )^2+(\frac{4}{5} )^2

z^2 = \frac{9}{25} + \frac{16}{25}

z^2=\frac{25}{25}

z^2=1

Taking square root on both the sides:

z=1

Now, sin\alpha=\frac{4}{5}

and we know that csc = \frac{1}{sin\alpha }

Therefore, csc = 5/4.

8 0
3 years ago
Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches. Which is the slant h
Nikitich [7]

Answer: 5 inches


Step-by-step explanation:

Given: Volume of clay = 48 cubic inches

If we make a solid square right pyramid with a base edge a= 6 inches.

Then its base area = a^2=6^2=36\ inches^2

we know that volume of square right pyramid=\frac{1}{3}\times\ a^2h

Therefore, volume of square right pyramid made by all of clay=\frac{1}{3}\times\ a^2h=48 cubic inches

\Rightarrow\frac{1}{3}\times\ (36)\times\ h=48\\\Rightarrow12h=48\\\Rightarrow\ h=4\ inches.....\text{[Divide 12 on both sides]}

Now, slant height l=\sqrt{(\frac{a}{2})^2+h^2}

\\\Rightarrow\ l=\sqrt{3^2+4^2}\\\Rightarrow\ l=\sqrt{9+16}\\\rightarrow\ l=\sqrt{25}\\\Rightarrow\ l=5

The slant height of the pyramid if Helen uses all the clay=5 inches

5 0
3 years ago
Read 2 more answers
Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t
Tresset [83]

Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = xyz

with subject to x+2y+3z=9

So, let z=\dfrac{9-x-2y}{3}

So, Volume becomes,

V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}

Partially derivative wrt x and y we get that

9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9

By solving these two equations, we get that

x=3,y=\dfrac{3}{2}

So, z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1

So, Volume of largest rectangular box would be

xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5

Hence, the volume of largest rectangular box is 4.5 units.

4 0
3 years ago
What are the coordinates of point B in the diagram?
Monica [59]
The correct answer would be (4,-5)
4 0
3 years ago
Read 2 more answers
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