If the volume of a frustrum is given as V = π h/3(R² + Rr + r²), find dV/dR.

Correct Answer is : πh3(2R+r)π h/3(2R + r)3πh(2R+r)

Correct Answer is : πh3(2R+r)π h/3(2R + r)3πh(2R+r)

Test Index

JAMB Mathematics 2019 Paper

Question : 48

Total: 73

V = \frac{\pi h}{3}(R^2 + Rr + r^2)

\frac{dV}{dR}

Solution:

Concept:

Differentiate the given volume formula with respect to

R

, treating

h

and

r

as constants.

Explanation:

Given:

V = \frac{\pi h}{3}(R^2 + Rr + r^2)

Expand the expression:

V = \frac{\pi h}{3}R^2 + \frac{\pi h}{3}Rr + \frac{\pi h}{3}r^2

Differentiate term by term with respect to

R

\frac{d}{dR}\left(\frac{\pi h}{3}R^2\right) = \frac{\pi h}{3}(2R) = \frac{2\pi h R}{3}

\frac{d}{dR}\left(\frac{\pi h}{3}Rr\right) = \frac{\pi h}{3}r

The last term

\frac{\pi h}{3}r^2

is constant, so its derivative is

0

Therefore:

\frac{dV}{dR} = \frac{2\pi h R}{3} + \frac{\pi h r}{3}

Factor out

\frac{\pi h}{3}

\frac{dV}{dR} = \frac{\pi h}{3}(2R + r)

Answer:

The correct answer is A.

\frac{\pi h}{3}(2R + r)

Go to Question:

Prev Question

Next Question