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Igoryamba
2 years ago
14

A sphere and a right cylinder have the same radius and volume. The cylinder has a height of 8 feet. Find the radius.

Mathematics
1 answer:
siniylev [52]2 years ago
8 0

9514 1404 393

Answer:

  6 feet

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr^2·h

For a sphere, the volume is ...

  V = 4/3πr^3

You want the volumes to be the same when h=8, so we have ...

  πr^2·8 = 4/3πr^3

Dividing by πr^2, we have ...

  8 = 4/3r

  r = 3/4·8 = 6

The radius is 6 feet.

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3 years ago
Need help ASAP. The diagram shows 5ft student standing near a tree. The shadow of the student and the shadow of the tree at endp
inna [77]

Answer:

The height of the tree = 25 feet

 Step-by-step explanation:  

From the given diagram : EF = 5 feet, FA = 8 feet, CA = 40 feet

∠AFE = 90° and ∠ACB = 90°

To find : CB, the height of the tree.  

Solution : In ΔAEF and ΔAB  C

∠AFE = ∠ACB = 90°  

∠A is common angle.  

So, By AA postulate of similarity of triangle, ΔAEF ~ ΔABC  

Now, sides of similar triangles are proportional to each other

\implies\frac{FA}{CA}=\frac{EF}{CB}\\\\\implies \frac{8}{40}=\frac{5}{CB}\\\\\implies CB=\frac{40\times 5}{8}\\\\\implies CB=25

Hence, The height of the tree = 25 feet

8 0
3 years ago
Use the net to find the surface area of the square pyramid. A) 210 in2 B) 320 in2 C) 420 in2 D) 450 in2
Aleksandr [31]

Answer:

D. 420

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\frac{1}{2} bh

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10×16= 160

160÷2=80

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multiply 80 by 4 to get 320

then find the surface area of the square by doing length×width to get 100

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320+100=420

4 0
3 years ago
Find the slope and the y- intercept of the line y=2x-6
Alchen [17]

Answer:

The slope is 2 and the y-intercept is -6

Step-by-step explanation:

we know that

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y=mx+b

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y=2x-6

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m=2

and

b=-6

<u><em>Verify</em></u>

For x=0

y=2(0)-6=-6 ---> is ok

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grin007 [14]

Answer:

This question is hot.

Step-by-step explanation:

6 0
2 years ago
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