Can the two integers both be positive? Explain

The cylinders are similar the volume of the larger cylinder is 1600 cubic centimeters what is the volume of the smaller cylinder

cestrela7 [59]

We are given Volume of the larger cylinder is = 1600 cubic centimeters.

Height of the larger cylinder = 16 cm.

We know formula of volume of a cylinder V= $\pi r^2h$ , where r is the radius of cylinder, h is the height of the cylinder.

Plugging value of V and h of larger cylinder, we get

$1600=\pi r^2(16).$

Dividing both sides by 16, we get

$\frac{1600}{16}=\frac{\pi r^2 (16)}{16}$

$r^2=100$

Taking square root on both sides, we get

r=10.

Therefore, radius of the larger cylinder is 10 cm.

We are given cylinders are similar .

<u>Note: The radii and heights of similiar cylinders are in same ratio.</u>

Therefore, we can setup a proportion:

Let us take radius of small cylinder is x.

$\frac{x}{10}=\frac{4}{16}$

$\frac{x}{10}=\frac{1}{4}$

Multiplying both sides by 10, we get

$10 \times \frac{x}{10}=10 \times\frac{1}{4}$

x=2.50.

Therefore, radius of the small cylinder = 2.5 cm.

Now, plugging radius =2.5 and height = 4 in the formula of volume the cylinder, we get

$V=\pi (2.5)^2(4)=\pi (6.25)(4) =25 \pi \ cm^3.$

Therefore, correct option is 25 pi cm^3.

8 0

3 years ago

Yesterday, Sharon read 14 pages of a book. Today, she continued reading the book at the same speed. She read 10 pages in 35 minu

horrorfan [7]

Answer:

Sharon spent a total of 49 minutes yesterday reading the book

Step-by-step explanation:

Step 1: Calculate the rate at which she reads

The total number of pages she reads at any given time interval can be expressed as;

T=P×m

where;

T=Total number of pages she reads

P=the rate at which she reads in number of pages per minute

m=total number of minutes she takes reading a book

In our case;

T=10 pages

P=p

m=35 minutes

replacing;

10=p×35

p=10/35

p=(10/35)

The rate at which she reads=(10/35) pages per minute

Step 2: Calculate the time she spent reading the book yesterday

Yesterdays variables are as follows;

T=14 pages

p=(10/35) pages per minute

m=unknown

replacing;

14=(10/35)×m

m=14×(35/10)

m=49

Sharon spent a total of 49 minutes yesterday reading the book

8 0

3 years ago

96 plus what equals 180?

Alisiya [41]

Answer:

Step-by-step explanation:

180-96

180-96 = 84

96 + 84 = 180

5 0

3 years ago

Read 2 more answers

What’s the translation from the graph y=6x^2 to the graph y=6(x+1)^2

Leno4ka [110]

For this case, the main function is given by:

$y = 6x ^ 2$

We can apply the following transformation:

Horizontal displacements:

Assume h> 0:

To graph f (x + h) move the graph of f (x) h units to the left.

For h = 1 we have:

$y = 6 (x + 1) ^ 2$

Answer:

the graph y=6(x+1)^2 is the graph y=6x^2 moved 1 unit to the left.

8 0

3 years ago

Find the equation of the linear function represented by the table below in slope-intercept form.

Degger [83]

Answer:

$y=10x-6$

Step-by-step explanation:

step 1

Find the slope

we have

(0,-6) and (1,4)

The slope is equal to

$m=(4+6)/(1-0)=10$

step 2

Find the equation of the line in slope intercept form

The equation of the line in slope intercept form is

$y=mx+b$

we have

$m=10$

$b=-6$ -----> y-intercept (given value in the table)

substitute

$y=10x-6$

4 0

3 years ago