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2 years ago

Please help me with this work

Mathematics

1 answer:

Dahasolnce [82]2 years ago

6 0

Answer:

about 243.9 cm³
35828 4/7 cm² = 3 102/175 m²

Step-by-step explanation:

The 8-cm diameter sphere has a radius of 4 cm. The volume of it is given by ...

V = 4/3πr³ = 4/3π(4 cm)³ = 256/3π cm³

The 8-cm cube has a volume of ...

V = s³

V = (8 cm)³ = 512 cm³

The volume of the empty space is the difference of these volumes:

space = 512 cm³ -256/3π cm³ = 256(6 -π)/3 cm³

space ≈ 243.9 cm³

The area of a hemisphere is twice the area of a circle with the same radius. Then the area of the top and bottom of the birdbath will be 2+1 = 3 times the area of a circle with radius 30 cm.

top+bottom area = 3 × πr² = 3 × 22/7(30 cm)² = 8485 5/7 cm²

The lateral area of the cylinder is ...

LA = 2πrh

= 2(22/7)(30 cm)(145 cm) = 27342 6/7 cm²

Then the total surface area of the birdbath is ...

total area = top+bottom area + lateral area

total area = 8485 5/7 cm² +27342 6/7 cm² = 35828 4/7 cm²

= 3 102/175 m²

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1. The mechanics at Lincoln Automotive are reborning a 6 in deep cylinder to fit a new piston. The machine they are using increa

Firdavs [7]

Answer:

$0.0239\frac{in^{3}}{min}$

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram of the cylinder. (See attached picture)

This diagram will help us visualize the problem better.

So we start by determining what data we already know:

Height=6in

Diameter=3.8in

Radius = 1.9 in (because the radius is half the length of the diameter)

The problem also states that the radius will increase on thousandth of an inch every 3 minutes. We can find the velocity at which the radius is increasing with this data:

$r'=\frac{1/1000in}{3min}$

which yields:

$r'=\frac{1}{3000}\frac{in}{min}$

with this information we can start solving the problem.

First, the problem wants us to know how fast the volume is increasing, so in order to find that we need to start with the volume formula for a cylinder, which is:

$V=\pi r^{2}h$

where V is the volumen, r is the radius, h is the height and π is a mathematical constant equal approximately to 3.1416.

Now, the height of the cylinder will not change at any time during the reborning, so we can directly substitute the provided height, so we get:

$V=\pi r^{2}(6)$

$V=6 \pi r^{2}$

We can now take the derivative to this formula so we get:

$\frac{dV}{dt}=2(6)\pi r \frac{dr}{dt}$

Which simplifies to:

$\frac{dV}{dt}=12\pi r \frac{dr}{dt}$

We can now substitute the data provided by the problem to get:

$\frac{dV}{dt}=12\pi (1.9) (\frac{1}{3000})$

which yields:

$\frac{dV}{dt}=0.0239\frac{in^{3}}{min}$

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3 years ago

Which expression has the sum of twenty six twentieths?

weeeeeb [17]

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7 0

3 years ago

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HELP EMERGENCY!!!! (2.5 x 10-10) (7 x 10-5)<br> Express your answer in scientific notation.

dangina [55]

Answer:

$1.75$ × $10^{-15}$

I hope this helps!

8 0

3 years ago

1. Write an algebra equation for each purchase. I (Mickey) bought an ice cream treat and a bottle of water for $10. Pam purchase

Ne4ueva [31]

x+y=10

x+2y=14
x is common in both so u have to subtract the second one from 1st
x-x + y-2y = 10-14
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3 years ago

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Elanso [62]

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7 0

3 years ago

Please help me with this work​

Please help me with this work