The expression $${\text{V}} = \int_0^{\text{H}} {\pi {{\text{R}}^2}{{\left( {1 - \frac{{\text{h}}}{{\text{H}}}} \right)}^2}} {\text{dh}}$$ for the volume of a cone is equal to
A. $$\int_0^{\text{R}} {\pi {{\text{R}}^2}{{\left( {1 - \frac{{\text{h}}}{{\text{H}}}} \right)}^2}} {\text{dr}}$$
B. $$\int_0^{\text{R}} {\pi {{\text{R}}^2}{{\left( {1 - \frac{{\text{h}}}{{\text{H}}}} \right)}^2}} {\text{dh}}$$
C. $$\int_0^{\text{H}} {2\pi {\text{rH}}{{\left( {1 - \frac{{\text{r}}}{{\text{R}}}} \right)}^2}} {\text{dh}}$$
D. $$4\int_0^{\text{R}} {\pi {\text{rH}}{{\left( {1 - \frac{{\text{r}}}{{\text{R}}}} \right)}^2}} {\text{dr}}$$
Answer: Option D
This Question Belongs to Engineering Maths >> Calculus
The Taylor series expansion of 3 sinx + 2 cosx is . . . . . . . .
A. 2 + 3x - x2 - \[\frac{{{{\text{x}}^3}}}{2}\] + ...
B. 2 - 3x + x2 - \[\frac{{{{\text{x}}^3}}}{2}\] + ...
C. 2 + 3x + x2 + \[\frac{{{{\text{x}}^3}}}{2}\] + ...
D. 2 - 3x - x2 + \[\frac{{{{\text{x}}^3}}}{2}\] + ...
B. \[\infty \]
C. \[\frac{1}{2}\]
D. \[ - \infty \]
A. \[1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
B. \[ - 1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
C. \[1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
D. \[ - 1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
Join The Discussion