If-part-of-the-curve-y-x-1-from-x-1-and-x-2-is-rotated-completely-about-the-y-axis-find-the-volume-of-the-solid-form-Mastermind-

Question Number 170412 by Mastermind last updated on 23/May/22

I f p a r t o f t h e c u r v e y = x + 1 f r o m x = 1

a n d x = 2 i s r o t a t e d c o m p l e t e l y a b o u t

t h e y - a x i s . f i n d t h e v o l u m e o f t h e

s o l i d f o r m .

M a s t e r m i n d

Answered by aleks041103 last updated on 23/May/22

T h e r e s u l t e d s h a p e i s a t r i n c a t e d c o n e .

r_{1} = 1, r_{2} = 2

h =∣ y_{2} - y_{1} ∣= 1

\Rightarrow V = \frac{1}{3} π h (r_{1}^{2} + r_{2}^{2} + r_{1} r_{2}) =

= \frac{1}{3} π (1 + 4 + 2) = \frac{7 π}{3}

\Rightarrow V = \frac{7 π}{3}

Commented by Mastermind last updated on 24/May/22

T h a n k s

Answered by MikeH last updated on 23/May/22

V = π \int_{a}^{b} y^{2} d x

\Rightarrow V = π \int_{1}^{2} (x^{2} + 2 x + 1) d x

V = π {[\frac{x^{3}}{3} + x^{2} + x]}_{1}^{2}

V = \frac{19 π}{3} cubic units

Commented by Mastermind last updated on 24/May/22

T h a n k y o u