Question

Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the other is five times greater. Find its radius. A. 22.5 cm. B. 6.36 cm. C. 0.90 cm. D. 7.69 c

Answer 1

Vol of sphere = 4/3 pi r^2.density of sphere = mass/volume.mass = densityxvolumesphere 1. mass = density x 4/3 pi 4.5^2sphere 2 5mass = density x 4/3 pi r^25=4/3 pi r^2 divided by 4/3 pi 4.5^25=r^2 divided by  4.5^25x4.5^2=r^2root(5x4.5^2)=r4.5 root 5 = r

Answer 2

Answer:

D) 7.69 cm

Explanation:

As we know that both the sphere must have same density

So the volume of first sphere

$V = \frac{4}{3}\pi r^3$

$V = \frac{4}{3}\pi(4.50)^3$

now the mass of this sphere is given as

$m = \rho V$

$m = \rho(\frac{4}{3}\pi (4.50)^3)$

now we know that mass of other sphere is 5 times more than this

so we will have

$m_1 = 5 m$

$\rho(\frac{4}{3}\pi r^3) = 5\rho(\frac{4}{3}\pi (4.50)^3)$

$r^3 = 5(4.50)^3$

$r = 7.69 cm$