If the volume of a sphere increases by 72.8 % | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the initial radius of the sphere be $r$ and the initial volume be $V = \frac{4}{3} \pi r^3$.After the increase,the new volume $V'$ is $V + 0.7

Vedclass · Accepted Answer

$44$

Vedclass · Answer

(B) Let the initial radius of the sphere be $r$ and the initial volume be $V = \frac{4}{3} \pi r^3$.After the increase,the new volume $V'$ is $V + 0.728V = 1.728V$.Since $V' = \frac{4}{3} \pi (r')^3$,we have $\frac{4}{3} \pi (r')^3 = 1.728 	imes \frac{4}{3} \pi r^3$.Thus,$(r')^3 = 1.728 r^3$,which implies $r' = \sqrt[3]{1.728} r = 1.2r$.The initial surface area is $S = 4 \pi r^2$ and the new surface area is $S' = 4 \pi (r')^2$.$S' = 4 \pi (1.2r)^2 = 4 \pi (1.44 r^2) = 1.44 S$.The percentage increase in surface area is $\frac{S' - S}{S} 	imes 100 = (1.44 - 1) 	imes 100 = 44 \%$.

If the volume of a sphere increases by $72.8 \%$,then its surface area increases by $... \%$

Similar Questions

If $A(3, -2, 2)$ and $B(2, \lambda+1, 5)$ are the end points of the diameter of a circle and the point $P(5, 6, -1)$ lies on the circle,then $\lambda=$

The equation of the sphere concentric with the sphere $2x^2 + 2y^2 + 2z^2 - 6x + 2y - 4z = 1$ and having double its radius is:

How many distinct spheres of radius $r$ can be drawn such that they touch all three coordinate planes?

If two spheres of radii $r_1$ and $r_2$ cut orthogonally,then the radius of the common circle is

If $r$ is the position vector of any point on a sphere and $a$ and $b$ are the position vectors of the extremities of a diameter,then which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module