Two spheres are cut from a certain uniform rock. One has radius 3.54 cm. The mass of the other is 3 times greater. Find its radius.
To find the radius of the second sphere, we can use the concept of the ratio of volumes.
The ratio of the volumes of two spheres is equal to the cube of the ratio of their radii.
Let's denote the radius of the second sphere as "r" (in cm).
Given:
Radius of the first sphere = 3.54 cm
Radius of the second sphere = r
Mass of the second sphere = 3 times greater than the mass of the first sphere.
Since the masses of the spheres are proportional to their volumes, we can write:
(volume of second sphere) / (volume of first sphere) = (mass of second sphere) / (mass of first sphere)
The mass is directly proportional to the volume, and the volume is directly proportional to the cube of the radius. Therefore, we can write:
[(4/3) * π * r^3] / [(4/3) * π * (3.54)^3] = 3 / 1
Simplifying the equation, we can cancel out the common terms:
(r^3) / ((3.54)^3) = 3
To isolate "r^3", we can cross-multiply:
(r^3) = 3 * ((3.54)^3)
Next, we can solve for "r" by taking the cube root of both sides:
r = ∛[3 * ((3.54)^3)]
Using a calculator, we can evaluate the expression on the right side to find the value of "r".
d *4/3 PI 3.54^3= 1/3*d *4PI/3 r^3
(d is density)
r^3=3.54^3 *3
r=3.54 * cubr(3)