A parametric curve defined by x-cos - u2 -y-sin - u2 in the range 0- u- 1 is rotated about the X-axis by 360 degrees- Area of the surface generated is

X=cos ( π u2 ) y=sin ( π u2 ) It represents a circle in x y plane. Given 0≤ u≤ 1. So, 0≤ x≤ 1, 0≤ y≤ 1 i.e., 0≤θ≤π2 So, we will get as quarter circle ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Engineering Mathematics

Solid of Revolution

A parametric ...

Question

A parametric curve defined by $x = c o s (\frac{π u}{2}), y = s i n (\frac{π u}{2})$ in the range $0 \leq u \leq 1$ is rotated about the $X -$ axis by $360$ degrees. Area of the surface generated is

\frac{π}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

π

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 π

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4 π

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $2 π$
$x = c o s (\frac{π u}{2})$
$y = s i n (\frac{π u}{2})$
It represents a circle in $x - y$ plane.

Given $0 \leq u \leq 1.$ So, $0 \leq x \leq 1, 0 \leq y \leq 1 i . e ., 0 \leq θ \leq \frac{π}{2}$
So, we will get as quarter circle in $x - y$ plane and by revolving it by $360^{o} w e w i l l g e t a h e m i s p h e r e o f u n i t r a d i u s . A r e a o f h e m i s p h e r e = 2 π (1)^{2} = 2 π$ .

Suggest Corrections

Similar questions

Q. Curve C is defined by the equation

y = \sqrt{(9 - x^{2})}

with

x \geq 0

. The area bounded by curve C, the x-axis and the y-axis is

Q. Area enclosed by the curve

y = f (x)

defined parametrically as

x = \frac{1 - t^{2}}{1 + t^{2}}, y = \frac{2 t}{1 + t^{2}}

is equal to :

Q. The part of straight line

y = x

between

x = 1

and

x = 2

is revolved about

X

-axis, then the curved surface area of the solid thus generated is

Q. The area bounded by the curve

y = {tan}^{2} x

and lines

x = 0, x = \frac{π}{4}

revolved about x-axis then volume of solid so generated is:

Q. Area enclosed by the curve

y = f (x)

that is being defined parametrically as

x = \frac{1 - t^{2}}{1 + t^{2}}

and

y = \frac{2 t}{1 + t^{2}}

(where

t \in R

) is equal to

Join BYJU'S Learning Program

A parametric curve defined by x=cos(πu2),y=sin(πu2) in the range 0≤u≤1 is rotated about the X−axis by 360 degrees. Area of the surface generated is

The correct option is C 2πx=cos(πu2) y=sin(πu2) It represents a circle in x−y plane. Given 0≤u≤1. So, 0≤x≤1,0≤y≤1i.e.,0≤θ≤π2 So, we will get as quarter circle in x−y plane and by revolving it by 360owe will get a hemisphere of unit radius.Area of hemisphere=2π(1)2=2π.

A parametric curve defined by $x = c o s (\frac{π u}{2}), y = s i n (\frac{π u}{2})$ in the range $0 \leq u \leq 1$ is rotated about the $X -$ axis by $360$ degrees. Area of the surface generated is