What’s the measure of str

A right circular cylinder is inscribed in a sphere with diameter 4cm as shown. If the cylinder is open at both ends, find the la

SOVA2 [1]

Answer:

$8\pi\text{ square cm}$

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

$S=2\pi rh$

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

$4^2 = (2r)^2 + h^2$ ( see in the below diagram ),

$16 = 4r^2 + h^2$

$16 - 4r^2 = h^2$

$\implies h=\sqrt{16-4r^2}$

Thus, the surface area of the cylinder,

$S=2\pi r(\sqrt{16-4r^2})$

Differentiating with respect to r,

$\frac{dS}{dr}=2\pi(r\times \frac{1}{2\sqrt{16-4r^2}}\times -8r + \sqrt{16-4r^2})$

$=2\pi(\frac{-4r^2+16-4r^2}{\sqrt{16-4r^2}})$

$=2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})$

Again differentiating with respect to r,

$\frac{d^2S}{dt^2}=2\pi(\frac{\sqrt{16-4r^2}\times -16r + (-8r^2+16)\times \frac{1}{2\sqrt{16-4r^2}}\times -8r}{16-4r^2})$

For maximum or minimum,

$\frac{dS}{dt}=0$

$2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})=0$

$-8r^2 + 16 = 0$

$8r^2 = 16$

$r^2 = 2$

$\implies r = \sqrt{2}$

Since, for r = √2,

$\frac{d^2S}{dt^2}=negative$

Hence, the surface area is maximum if r = √2,

And, maximum surface area,

$S = 2\pi (\sqrt{2})(\sqrt{16-8})$

$=2\pi (\sqrt{2})(\sqrt{8})$

$=2\pi \sqrt{16}$

$=8\pi\text{ square cm}$

4 0

3 years ago

Pls help, write an equation then solve for x

tamaranim1 [39]

Answer:

x= $\frac{1}{6}n+\frac{\sqrt{2} }{4}$

Step-by-step explanation:

mutiply both sides of the equation by 6

12x-2n=3 $\sqrt{2$

move the bariable to the right hand side and change its sign

12x=3 $\sqrt{2$ +2n

divide both sides

x= $\frac{\sqrt{2} }{4}$ +1/6n

use commutative propert to reorder the terms

x= 1/6n + $\frac{\sqrt{2} }{4}$

and thats it, i hope this helps ya!

4 0

2 years ago

Sam is practicing long track speed skating at an ice skating rink. The distance around the rink is 250 yards. He has skated arou

goldenfox [79]

Answer:

He needs to complete a distance of 4,030 yards around the rink to make a total skating distance of 3 miles

Step-by-step explanation:

In this question, we are asked to calculate the number of yards needed to complete 3 miles skating around a rink.

We proceed as follows;

First, we can see he has skated 5 times around a rink that has a distance of 250 yards. His total distance covered would be 250 * 5 = 1250 yards

Now he is looking at completing 3 miles, we need to know the number of yards in 3 miles.

Mathematically, 1 mile = 1760 yards

3 miles = 3 * 1760 = 5,280 yards

To know the number of yards he need to skate more, we simply carry out a subtraction;

5,280 yards - 1250 yards = 4,030 yards

5 0

3 years ago

Can some help me plz

Stels [109]

Answer:

$\sqrt{2}$

Step-by-step explanation:

Apply the 30-60-90 formula

side between 60 and 90 is x

side between 90 and 30 is $x\sqrt{3}$

side between 90 and 30 is 2x

If $x\sqrt{3}$ = $\sqrt{6}$ then x= $\sqrt{2}$

5 0

3 years ago

PLEASE HELP WITH THE QUESTION BELOW ASAP!! THANKS SO MUCH!

Morgarella [4.7K]

Answer:

y=-1/4x-4

Step-by-step explanation:

it simple rise over run: -1 go down one over 4 right or the other way around go up 1 and left 4 either way would work your y intercept is -4 because that is the point crossing the y-axis hope i helped!

7 0

3 years ago

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