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charle [14.2K]
3 years ago
7

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 30 m

Mathematics
1 answer:
podryga [215]3 years ago
4 0

Answer:

The volume of the sphere is 20 m

Step-by-step explanation:

Given

Solid Shapes: Cylinder and Sphere

Volume of the cylinder = 30m^3

Required

Volume of the sphere

First, we need to calculate the radius of the cylinder

The formula goes thus

V = \pi r^2h

By substituting 30 for V, we have

30 = \pi r^2h

Divide through by h

\frac{30}{h} = \frac{\pi r^2h}{h}

\frac{30}{h} = \pi r^2

Calculating the volume of the sphere

The formula goes thus

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

Expand Expression

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

Substitute \frac{30}{h} = \pi r^2

V = \frac{4}{3} * \frac{30}{h} * r

Simplify Expression

V = \frac{4}{1} * \frac{10}{h} * r

V =  \frac{40}{h} * r

Given that the height of the cylinder and the sphere are equal

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

Mathematically; This is represented by

h = D

Where D represents diameter of the sphere

Recall that D = 2r (2 * radius)

Substitute 2r for D

h = 2r

Substitute h = 2r in V =  \frac{40}{h} * r; This gives

V =  \frac{40}{2r} * r

V =  \frac{40r}{2r}

V =  20

Hence, the volume of the sphere is 20 m

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If you add 40 + 50 + 60 together you get 150. These can not be the angle measures of interior angles of a triangle because the sum is less then 180.

If you add 15 +30 + 135 together you get 180! This set of angle measures can the be interior angles of a triangle!

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If the perimeter of a square is 20, what is the length of the diagonal ?
Rina8888 [55]

Answer:

Step-by-step explanation:

if you know that the perimeter is 20,

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20/4=5.

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Use Pythagorean formula

Then know that a2+b2=c2

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7 0
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Find the value of X
vredina [299]

Answer:

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Step-by-step explanation:

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QPR + RPS = 180

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Subtract 100 from each side

10x = 180-100

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Divide by 10

x =80/10

x = 8

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3 years ago
If $17,000 is invested in an account for 25 years. Calculate the total interest earned at the end of 25 years if the interest is
KATRIN_1 [288]

Answer:

a.) $29,750.00   simple interest

b.) $75,266.35  Compounded annually

c.) $79,358.65 compunded  quarterly

d.) $80,332.11 compounded monthly

Step-by-step explanation:

a.) Formula: I = p x r x t

Where:

P is the principal amount, $17000.00.

r is the interest rate, 7% per year, or in decimal form, 7/100=0.07.

t is the time involved, 25....year(s) time periods.

So, t is 25....year time periods.

To find the simple interest, we multiply 17000 × 0.07 × 25 to get that:

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______________________________

b.) $75,266.35

c.) $79,358.65

d.) $80,332.11

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