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Alexxx [7]
3 years ago
14

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 pi feet cubed.

Mathematics
1 answer:
LenaWriter [7]3 years ago
4 0

Answer:

C. V = two-thirds (27)

Step-by-step explanation:

Given

Solid Shapes: Cylinder and Sphere

Volume of Cylinder = 27π ft³

Required

Volume of the sphere.

From the question,

<u>We have that</u>

1.  The volume of the sphere is the same as the volume of the cylinder

2. The height of the sphere is the same as the height of the cylinder.

From (2) above;

This means that the height of the cylinder equals the diameter of the sphere.

Let h represent the height of the sphere and d represent the diameter of sphere.

Mathematical, d = h

Recall that radius, r = r = \frac{d}{2}

Substitute h for d in the above expression

r = \frac{h}{2}. ----- (take note of this)

Calculating the volume of a cylinder.

V = πr²h

Recall that  V = 27; This gives us

27 = πr²h

Divide both sides by h

\pi r^2 = \frac{27}{h}

-------------------

Calculating the volume of a sphere

V = \frac{4}{3}\pi r^3

Expand the above expression

V = \frac{4}{3}\pi r^2 * r

Substitute \pi r^2 = \frac{27}{h}

V = \frac{4}{3} * \frac{27}{h} * r

Recall that r = \frac{h}{2}

So,

V = \frac{4}{3} * \frac{27}{h} * \frac{h}{2}

V = \frac{4}{3} * \frac{27}{2}

V = \frac{2}{3} * 27

V = \frac{2}{3} (27)

V = two-third (27)

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Mario can eat 21 hot dogs in 6 minutes. At the same place, how many minutes would it take him to eat 35 hot dogs? ​
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Answer:

10 minutes

Step-by-step explanation:

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Let 35 hot dog  eats in x minutes :

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6 0
3 years ago
The proof diagram to complete the question state the missing reason in the proof for the letter given
melisa1 [442]

ANSWER

First proved that line p is parallel to line r

to proof

As given in the question

∠1 ≈∠5

∠1 and ∠5 are corresponding angles

by using the property of the corresponding angles

 two lines are cut by a transversal so that the corresponding angles are


congruent, then these lines are parallel.


As shown in diagram q is transversal line.

Thus by using the above property

line p is parallel to line r.

proof of 1(a)

REASON

Vertically opposite angle

The pair of angles formed when two lines intersect each other are called vertically opposite angles.

Thus

∠4 and ∠1 are vertically opposite angle

thus

∠4 ≈∠ 1

proof of 2(b)

REASON

Alternate interior angle

the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles . If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent .

as line p is parallel to line r (proof above)

q is transversal

thus

∠4 ≈∠ 5

Hence proved

proof of 3 (c)

As ∠4 ≈∠5 (proof above)  

REASON

If two lines are cut by a transversal so that the alternate interior angles

are congruent, then these lines are parallel.

Thus by above property

line p is parallel to line r

Hence proved







4 0
3 years ago
Read 2 more answers
I need help with this equation
OlgaM077 [116]

Step-by-step explanation:

whats the equation lol

4 0
3 years ago
Read 2 more answers
Please help me please please
LenKa [72]

Answer:

1276.19553 m^{2}

Step-by-step explanation:

First, find height using Pythagoras thorem.

a=\sqrt{20^2+12.5^2}

a=15.61

Then use the formula to find the surface area of a cone.

π•12.5•(12.5+\sqrt{15.61^2+12.5^2})=1276.19553 m^{2}

6 0
2 years ago
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