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4 years ago

If the radius and the height of a right cylinder are both doubled, by what factor will the surface area increase?

Mathematics

1 answer:

Romashka [77]4 years ago

3 0

Answer:

Doubling the radius and the height of a right cylinder will increase the value of its surface area by a factor of 4

Step-by-step explanation:

Mathematically, the surface area of a right cylinder can be calculated using the formula;

A = 2 π r (r + h)

now let’s double the radius and the height.

Our new r becomes 2r and our new height becomes 2h. Substituting these into the area formula, we have

A = 2 π (2r)( 2r+ 2h)

Let’s factor out all the 2 , we have

A = 4 π r (2(r+h))

A = 8 π r( r + h)

we can see that the value of the area has been increased by a factor of 4

You might be interested in

The ratio of boys to girls on a swimming team is 4 to 3. The team has 35 members how many are girls

diamong [38]

Answer:

See below:

Step-by-step explanation:

Hello! I hope you are having a nice day. My name is Galaxy and I will be helping you today!

We can solve this problem in two steps, one being Comprehension and another being Solving. I'll start off with Comprehension.

Comprehension

We can see that based of the problem, for every batch of 7 kids, there are 4 boys and 3 girls. That means that we can split the total, which is 35, into groups of 7 and seeing how many girls and boys there are.

Now that we know what we need to figure out and what to do, we can begin solving.

Solving

So, for every group of 7 kids there are 4 boys and 3 girls. We can divide 35 by 7 to find how many of these identical groups there are.

$35 \div 7=5$

We know that there are 5 such groups of 4 boys and 3 girls each. Therefore, we can multiply 4 and 3 by 5 as there are 5 such groups to find our total.

$4*5=20\\$

We know there are 20 boys.

$3*5=15$

We know there are 15 girls.

We can check this by seeing if this adds up,

$15+20=35?\\35=35$

Therefore, our answer is there are 15 girls and 20 boys.

5 0

3 years ago

Read 2 more answers

Mikes movie Rentals Charge $3.00 for each rental plus $0.50 for each additional day. Reed's Rentals Charge $1.50 each rental plu

iris [78.8K]

Answer:

Step-by-step explanation:

What we need here is to express both charges trough equations, and then find out for which value these equations are equal.

Let X be the amount of additional days of rent.

So, Mikes Movie Rentals cost equations is:

CostMike = 3 + 0.5X

This implies that if there is no additional day (X=0), the cost is $3, if there is one additional day the cost is $3.5, for 2 days $4, and so on ...

Now lets find Reed's Rental cost.:

CostReed = 1.5 + 1.25X

And the interpretation is analogous to the one above. If there is no additional day, Reed's charge is $1.5, for 1 days $2.75, for 2 days $4

(Notice that with the examples I made about interpreting the equations I found out that for 2 days the cost of both is the same. Now lets find it analytically)

For finding the additional days that give the same costs we need to equal both equations:

3 + 0.5 X = 1.5 + 1.25 X

Lets subtract 1.5 from both sides:

3 - 1.5 + 0.5 X = 1.5 - 1.5 + 1.25 X

1.5 + 0.5 X = 1.25 X

Now subtract 0.5 X in both sides:

1.5 + 0.5 X - 0.5 X = 1.25 X - 0.5 X

1.5 = 0.75 X

Dividing both sides by 0.75:

1.5 / 0.75 = 0.75 X / 0.75

2 = X

So, for 2 additional days bith charges are equal.

6 0

3 years ago

Help me please thank you so much if you did

Gala2k [10]

Answer:

I just answed this question today!Your asnwer is 144.

Step-by-step explanation:

1:5:3

48 total.

Divide 48 and get 16

Multiply 16 x1

Multiply 16 x5

Multiply 16x 3

16:80:48

4 0

3 years ago

Read 2 more answers

You borrowed $25 from your friend. You paid him back in full after 6 months. He charged $2 for interest. What was the annual sim

Paraphin [41]

$\bf \qquad \textit{Simple Interest Earned}\\\\
I = Prt\qquad 
\begin{cases}
I=\textit{interest earned}\to &\$2\\
P=\textit{original amount}\to& \$25\\
r=rate \\
t=years\to &\frac{1}{2}
\end{cases}$

bearing in mind, "t" is in years, 6months is just 1/2 year

solve for "r", you'd get a decimal amount, multiply times 100, to get the percentage form

5 0

4 years ago

Read 2 more answers

Me need more help plz also add explanation real explanation

Reika [66]

So we want to find the surface area of this pyramid. Finding the surface area of a 3D shape is essentially finding the area of all its sides and adding them together.

What we're going to have to do here is find the area of the base of the pyramid, which is basically a square, and find the area of all four sides of the pyramid, which are triangles.

Formula for area of a square: length × width

Formula for area of a triangle: (base × height) ÷ 2

First we will find the area of the base:

l × w = A

(Write out formula)

8 × 8 =

(Input values)

A = 64 m^2 (square meters or meters squared)

(We have our answer, dont forgot to write your units.)

So we've figured out the area of the base. Now onto the triangles:

(b×h) ÷ 2 = A

(Write out formula)

(8 × 6) ÷ 2 =

(Input values)

48 ÷ 2 =

(Use PEMDAS to solve this correctly. We did whatever was in the parenthesis first, which was multiplication.)

A = 24m^2 (square meters or meters squared)

(We have our answer.)

Now we've found the area of the base of the pyramid and one of the sides of the pyramid, but we're almost done! There's four sides to the pyramid, they're all the same. So since we found the area for one, we can multiply that by 4 to find the area of all sides added together:

24 × 4

(area of a side × total sides)

= 96m^2

All that's left is adding the 96 to the area of the base to get our total surface area of the pyramid:

96 + 64 = 160

The surface area of the pyramid is 160m^2(square meters or meters squared)

(Hope this helps :) )

8 0

3 years ago

Read 2 more answers