# cylinder....... help

A circular cylinder is inscribed in a given cone of radius R cm and height H cm as shown in the figure Find the curved surface area S of the circular cylinder as a function of x Find the relation connecting x and R when S is maximum

Note by Sonali Sukesh
4 years, 11 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

By Similarity of Triangles,
$$\displaystyle \frac{h}{R-x} = \frac{H}{R}$$

$$\displaystyle\Rightarrow h = \frac{H}{R} (R-x)$$

Now, it is clear that,
$$\displaystyle S = 2\pi x\times h$$

Substitute the value of $$\displaystyle h$$ and get $$\displaystyle S$$ as a function of $$\displaystyle x$$.

Differentiate the function that you just derived wrt $$\displaystyle x$$, and put it equal to $$\displaystyle 0$$.

You will find a relation between $$\displaystyle x$$ and $$\displaystyle R$$.

- 4 years, 11 months ago

Right.

- 4 years, 11 months ago

2pixh = S, x = R(1-h/H)..............................................................(when S is maximum)

- 4 years, 11 months ago

S = 2pix ; x= R[1-h/H]

- 4 years, 11 months ago

need help fast

- 4 years, 11 months ago

put H/R =k k=(H-h)/x from this h=H-kx after this S=2pixh put h=H-kx differentiate with respect to x and put dS/dx=0 from this x=R/2

- 4 years, 11 months ago

thanks 2 all

- 4 years, 11 months ago

right 2pixh = S, x = R(1-h/H)..........(when S is maximum)

- 4 years, 11 months ago