Differential and Integral Calculus Questions and Answers – Volume of Solid of Revolution

«
»

This set of Differential and Integral Calculus Interview Questions and Answers for freshers focuses on “Volume of Solid of Revolution”.

1. The volume of solid of revolution when rotated along x-axis is given as _____________
a) \(\int_a^b πy^2 dx \)
b) \(\int_a^b πy^2 dy \)
c) \(\int_a^b πx^2 dx \)
d) \(\int_a^b πx^2 dy \)
View Answer

Answer: a
Explanation: Volume is generated when a 2d surface is revolved along its axis. When revolved along x-axis, the volume is given as \(\int_a^b πy^2 dx \).
advertisement

2. The volume of solid of revolution when rotated along y-axis is given as ________
a) \(\int_a^b πy^2 dx \)
b) \(\int_a^b πy^2 dy \)
c) \(\int_a^b πx^2 dx \)
d) \(\int_a^b πx^2 dy \)
View Answer

Answer: d
Explanation: Volume is generated when a 2d surface is revolved along its axis. When revolved along y-axis, the volume is given as \(\int_a^b πx^2 dy \).

3. What is the volume generated when the ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) is revolved about its minor axis?
a) 4 ab cubic units
b) \(\frac{4}{3} a^2 b \) cubic units
c) \(\frac{4}{3} ab \) cubic units
d) 4 cubic units
View Answer

Answer: b
Explanation: y- axis is the minor axis. \(x^2 = \frac{a^2}{b^2} (b^2 – y^2)\)
\(V = \int_a^b πx^2 dy\)
\(= \int_{-b}^b π \frac{a^2}{b^2} (b^2 – y^2) \,dy \)
\(= 2π \frac{a^2}{b^2} \Big(b^2 y- \frac{y^3}{3}\Big)_0^b \)
\(= 2π \frac{a^2}{b^2} (b^3- \frac{b^3}{3}) \)
\(= \frac{4}{3} a^2 b \) cubic units.

4. What is the volume generated when the region surrounded by y = \(\sqrt{x}\), y = 2 and y = 0 is revolved about y – axis?
a) 32π cubic units
b) \(\frac{32}{5} \) cubic units
c) \(\frac{32π}{5}\) cubic units
d) \(\frac{5π}{32} \) cubic units
View Answer

Answer: c
Explanation: Limits for y -> 0,2 x = y2
\(Volume = \int_a^b πx^2 dy\)
\( = \int_0^2 πy^4 dy\)
\( = \Big[\frac{πy^5}{5}\Big]_0^2\)
\( = \frac{32π}{5}\) cubic units.
advertisement

5. What is the volume of the sphere of radius ‘a’?
a) \(\frac{4}{3} πa \)
b) 4πa
c) \(\frac{4}{3} πa^2 \)
d) \(\frac{4}{3} πa^3 \)
View Answer

Answer: d
Explanation: The equation of a circle is x2 + y2 = a2
When it is revolved about x-axis, the volume is given as
\(V = 2 \int_a^b πy^2 dy\)
\(= 2 \int_0^a π(a^2-x^2) dx\)
\(= 2π \Big(a^2 x – \frac{x^3}{3}\Big)_0^a\)
\(= \frac{4}{3} πa^3.\)

6. Gabriel’s horn is formed when the curve ____________ is revolved around x-axis for x≥1.
a) y = x
b) y = 1
c) y = 0
d) y = 1/x
View Answer

Answer: d
Explanation: Gabriel’s horn or Torricelli’s Trumpet is a famous paradox. It has a finite volume but infinite surface area.

Sanfoundry Global Education & Learning Series – Differential and Integral Calculus.

advertisement

To practice all areas of Differential and Integral Calculus for Interviews, here is complete set of 1000+ Multiple Choice Questions and Answers.

Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

advertisement
advertisement
advertisement
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn