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Troyanec [42]
2 years ago
10

Antoine has a solid, spherical ball of clay with a radius of 5 cm. If he shapes it into a solid, cone–shaped figure with a radiu

s of 2 cm, what will the height of the cone be?
Mathematics
1 answer:
weqwewe [10]2 years ago
3 0

Answer:

Step-by-step explanation:

We'll call height h.

The equations of a cone and sphere are:

Cones: 1/3 * base area * h

Spheres: 4/3 π * r³

The base area of a cone would be the area of a circle equation:

π * r² = π * 2² = 4π.

Because you're converting from sphere to cone, you would set their equations equal to each other.

1/3 * 4π * h = 4/3 π * 5³

Next, isolate h.

h = (4/3 π * 5³)/(1/3 * 4π)

h = 125

Hope this helps!

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Please help I will give brainliest
lutik1710 [3]

Answer:

Angle PQW is equal to 35 degrees

Step-by-step explanation:

Angle PQW = 36x - 1

Angle WQR = 134x

Angle PQR = 169 degrees

To find angle PQW, Set Angles PQR and WQR to PQW. The equation should look like this:

PQR - WQR = PQW

Substitute in the values

169 - 134x = 36x - 1

Now add 134x to both sides and add 1 to both sides.

170 = 170x

Now divide 170 from both sides

x = 1

Plug x into angle PQW

36(1) - 1 = 35

6 0
2 years ago
HELP 10 POINTS AND BRAINLIEST The triangles below are similar. In each traingle there is a 53°angle and a right angle. What is t
Mrrafil [7]

Answer:

Step-by-step explanation:

Since both triangles are similar, we know this because they have 2 angles in common, they both have the same third angle.

To find the third angle, we use the angle sum. The sum of angles in a triangle will always equal 180 degrees. We are given a right angle which is 90 degrees and another angle, which is 53 degrees. Knowing this:

90 + 53 + x = 180 (I have chosen to call the third angle x)

when rearranging this we get

180 - 90 - 53 = x

now we solve

x = 37 degrees

Hope this helps,

Cate

8 0
2 years ago
Read 2 more answers
Use polar coordinates to find the volume of the given solid. bounded by the paraboloid z = 9 + 2x2 + 2y2 and the plane z = 15 in
mina [271]

Answer:

Z = 8 + 2x2 + 2y2

Convert to polar coordinates

Z = 8 + 2r2

Now theta will go from 0 to pi/2 because it's in the first quadrant.

R will go from 0 to the radius of the circle formed at the intersection of the plane and the paraboloid.

14 = 8 + 2r2

r = sqrt(3)

So r goes from 0 to sqrt(3).

You integrate 14-z where 0<r<sqrt(3) and 0<theta<pi/2.

It is 14-z and not z because just z would give the volume under the paraboloid.

Step-by-step explanation: please go answer my recent question

5 0
2 years ago
Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar pe
Nutka1998 [239]
Helena can make 2 loaves of  bread and 4 batches of muffins.
6 0
2 years ago
Read 2 more answers
Jenna mixed two shades of purple paint. For Purple People Eater, she used 3 pints of red paint for every 5 pints of blue paint.
emmasim [6.3K]

Answer:

\frac{12}{35}

Step-by-step explanation:

Given :

→ For Purple People Eater, she used 3 pints of red paint for every 5 pints of blue paint.

i.e, The ratio of red paint to blue paint is 3:5

→ For Purple Majesty, she used a blue to red paint ratio of 7 to 4.

i.e, The ratio of red paint to blue paint is 4:7

To find :

1) Compare the ratios of red paint to blue paint.

\frac{3}{5}\times \frac{4}{7}=\frac{12}{35}

2) The ratio for Purple People Eater can be expressed in fraction form as :

=\frac{3}{5}

3) The ratio for Purple Majesty can be expressed in fraction form as :

=\frac{7}{4}

4) To compare these fractions, rewrite them with a common denominator

For common denominator

Multiply numerator and denominator by 4 in \frac{3}{5}

\Rightarrow\frac{3\times 4}{5\times4}=\frac{12}{20}

Multiply numerator and denominator by 5 in \frac{7}{4}

\Rightarrow\frac{7\times 5}{5\times4}=\frac{35}{20}

Common denominator is 20


6 0
2 years ago
Read 2 more answers
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