## Active forum topics

- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Eliminate the Arbitrary Constants
- Law of cosines
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Integration of 4x^2/csc^3x√sinxcosx dx
- application of minima and maxima
- Sight Distance of Vertical Parabolic Curve
- Application of Differential Equation: Newton's Law of Cooling

## New forum topics

- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Integration of 4x^2/csc^3x√sinxcosx dx
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Newton's Law of Cooling
- Law of cosines
- Can you help me po to solve this?
- Eliminate the Arbitrary Constants
- Required diameter of solid shaft

## Recent comments

- Hello po! Question lang po…1 week 5 days ago
- 400000=120[14π(D2−10000)]

(…1 month 2 weeks ago - Use integration by parts for…2 months 2 weeks ago
- need answer2 months 2 weeks ago
- Yes you are absolutely right…2 months 2 weeks ago
- I think what is ask is the…2 months 2 weeks ago
- $\cos \theta = \dfrac{2}{…2 months 2 weeks ago
- Why did you use (1/SQ root 5…2 months 2 weeks ago
- How did you get the 300 000pi2 months 2 weeks ago
- It is not necessary to…2 months 2 weeks ago

## Re: volumes of solids of revolution

Volume generated when the area is rotated about the line x = 9$V = 2\pi {\displaystyle \int_a^b} R \, dA$

$V = 2\pi {\displaystyle \int_{x_1}^{x_2}} (9 - x)(y \, dx)$

$V = 2\pi {\displaystyle \int_0^9} (9 - x)(\sqrt{x} \, dx)$

$V = 129.6\pi ~ \text{unit}^3$

Volume generated when the area is rotated about the line y = 3$V = \pi {\displaystyle \int_{x_1}^{x_2}} ({R_{\text{outer}}}^2 - {R_{\text{inner}}}^2) \, dx$

$V = \pi {\displaystyle \int_0^9} \left[ 3^2 - (3 - y)^2 \right] \, dx$

$V = \pi {\displaystyle \int_0^9} \left[ 9 - (3 - \sqrt{x})^2 \right] \, dx$

$V = 67.5\pi ~ \text{unit}^3$

## Re: volumes of solids of revolution

In reply to Re: volumes of solids of revolution by Jhun Vert

Thank you po

## Re: volumes of solids of revolution

Solution by Pappus's Theorem$A = \frac{2}{3}(3)(9) = 18 ~ \text{unit}^2$

$\bar{x} = \frac{2}{5}(9) = 3.6 ~ \text{units}$

$\bar{y} = \frac{3}{8}(3) = 1.125 ~ \text{units}$

Volume generated when the area is rotated about the line x = 9$V = 18 \times 2\pi (3.6)$

$V = 129.6\pi ~ \text{unit}^3$

Volume generated when the area is rotated about the line y = 3$V = 18 \times 2\pi (3 - 1.125)$

$V = 67.5\pi ~ \text{unit}^3$

## Re: volumes of solids of revolution

pasagot nga po ulit ito..thanks