All categories

3 years ago

What is the ratio for the surface areas of the cones shown below, given that

Mathematics

1 answer:

andreyandreev [35.5K]3 years ago

5 0

Answer:

The ratio for the surface areas is equal to 4

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z -----> the scale factor

In this problem

The scale factor is equal to

$z=\frac{2}{1}$ ----> the ratio of its corresponding radii or its corresponding altitudes

step 2

Find the ratio for the surface areas of the cones

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the surface area of the larger cone

y ----> the surface area of the smaller cone

$z^{2} =\frac{x}{y}$

we have

$z=\frac{2}{1}$

substitute

$(\frac{2}{1})^{2}=\frac{x}{y}$

$4=\frac{x}{y}$

The ratio for the surface areas is equal to 4

That means-----> The surface area of the larger cone is 4 times the surface area of the smaller cone

You might be interested in

G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =

Svetach [21]

Presumably you should be doing this using calculus methods, namely computing the surface integral along $\mathbf r(u,v)$ .

But since $\mathbf r(u,v)$ describes a sphere, we can simply recall that the surface area of a sphere of radius $a$ is $4\pi a^2$ .

In calculus terms, we would first find an expression for the surface element, which is given by

$\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k$
$\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j$
$\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k$
$\implies\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|=a^2\sin u$

So the area of the surface is

$\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u$
$=-2\pi a^2(\cos\pi-\cos 0)$
$=-2\pi a^2(-1-1)$
$=4\pi a^2$

as expected.

6 0

3 years ago

8 miles is approximately equal to 6 km. How many km are equal to 28 miles? How many miles are equal to 42 km?

Pani-rosa [81]

1 mile = about 1 1/3 km because 8/6 = 1 1/3
so 28 times 1 1/3 = 37 1/3 (first answer)

42 / 6 = 7
7 miles are in 42 km (2nd answer)

3 0

4 years ago

hii how are yall doing me im ok ig.... i.dk anymore also plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help ty

lora16 [44]

Answer:

Step-by-step explanation:

j=+

We move all terms to the left:

j-(+)=0

We add all the numbers together, and all the variables

j-0=0

We add all the numbers together, and all the variables

j=0

7 0

3 years ago

Javier owns 200 shares on one company. On Tuesday, the stock price dropped $19 per share. What was the total change in value of

katrin [286]

Answer:

-$3800

Step-by-step explanation:

Javier lost $19 on each of his 200 shares, so his total loss was ...

... 200 shares × $19/share = $3800

The portfolio lost $3800 in value on Tuesday.

8 0

3 years ago

Some one plz tell me how to do this

goldenfox [79]

Subtract the 18 from the 78 then multiply both sides by -1, then divide by 5.

8 0

3 years ago

Read 2 more answers