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Dafna1 [17]
3 years ago
9

A sphere with a radius of 6cm has the same volume as a cylinder with a height of 4.5cm. What is the radius of the cylinder

Mathematics
1 answer:
yawa3891 [41]3 years ago
4 0
Short answer: r = 8
Remark
The easiest way to do this is to solve the sphere's volume in terms of pi. When you do this, you can equate that to the formula for a cylinder and cancel the pi values. 

Step One
Find the volume of the sphere.

<em>Givens</em>
r = 6 cm

<em>Formula</em>
V = (4/3) pi r^3

<em>Sub and Solve</em>
V =  4/3 pi * 6^3
V = 288 * pi

Step two 
Find the radius of the cylinder

<em>Givens</em>
V = 288* pi cm^3
h = 4.5 cm

<em>Formula</em>
V = pi r^h

<em>Sub and solve</em>
288 pi cm^3 = pi r^2 * 4.5    Divide both sides by pi
288 cm^3 = 4.5 r^2              Divide both sides by 4.5
388 / 4.5 = r^2
64 = r^2                                Take the square root of both sides.
r = square root( 64)
r = 8 <<<<< Answer

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Step-by-step explanation:

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AB is congruent to DE because segment DE was constructed so that DE = AB. BC is congruent to EF because segment EF was construct
Alex Ar [27]

DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.

<h3>Congruent shape</h3>

Two shapes are said to be congruent if they have the same shape, all their corresponding angles and sides are congruent to one another.

Given that DE = AB and BC = EF.

In right triangle DEF, using Pythagoras:

DF² = DE² + EF²

Also, In right triangle ABC, using Pythagoras:

AC² = AB² + BC²

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6 0
2 years ago
Carlos had 7¾ cups of cheese. After making 5 pizzas, he now only has 2 cups of cheese. How much cheese did Carlos use?
Musya8 [376]

Answer:

5 3/4 cups of cheese used for the pizza

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4 0
2 years ago
BRAINLIEST ANSWER!!
Maksim231197 [3]

Answer:

1. 30(8.75) + 11t = 400

2. 12.5 hours

Step-by-step explanation:

1. What is given is you work for 30 hours per week at a gas station for $8.75 an hour. You also work as a landscaper for $11 an hour. You want to a make a total of $400 per week.

30 hours and $8.75 an hour would be equivalent to 30(8.75)

We don’t know how many hours you work as a landscaper but you earn $11 an hour, which is equivalent to 11t

Finally, you want to earn a total of $400 a week, which means the sum equals 400

30(8.75) + 11t = 400

2. 30(8.75) = 262.5

400 - 262.5 = 137.5

137.5 / 11 = 12.5

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