Question

QUESTION 8 The region enclosed by the curves y=x3, y=0, and x = 2 is revolved about the x-axis. What is the volume of the resulting solid? O 32 - TT 3 96 5 TT 0 471 128 TT 7 64 TT

Answer 1

$\text{ Given curves are }$

Y = 1, | = 0,,L = 2

$\text{ In the given region, }x \text{ is varies frrom }x =0 \text{ to }x =2$

$\text{Region enlosed by given curves is revolved about x -axis }$

$\text{Radius of resulting solid will be given by }$

$\text{Volume of resulting solid will be given by }$

$V =\int_0^2 \pi (R^2(x))dx =\int_0^2 \pi (x^3)^2dx =\pi\int_0^2 x^6dx$

$=> V =\pi \left ( \frac{x^7}{7} \right )_0^2 =\pi \left ( \frac{2^7}{7} -\frac{0^7}{7} \right )$

$=> V =\frac{128 \pi}{7}$