A cone with base radius of 5 cm and height of 20 cm is filled with

oil with specific gravity of
0.85.
Determine
the
dimension
of
cubic
steel which its weight is equivalent to the oil
weight. Steel
Specific Gravity is
7.1

volumesteel=.85/7.1 * volume cone

volumesteel=.85/7.1 * 1/3 *(pi*25)20

so the edge of a cube of steel would be the cubic root of that.

To determine the dimensions of the cubic steel that has the same weight as the oil, we need to find the weight of the oil first.

The volume of a cone is given by the formula: V = (1/3)πr^2h, where r is the base radius and h is the height.

Given that the base radius (r) of the cone is 5 cm and the height (h) is 20 cm, we can calculate the volume of the cone as follows:

V = (1/3)π(5^2)(20)
V ≈ 523.6 cm^3

Now, to find the weight of the oil, we multiply the volume by the specific gravity of the oil. The weight of the oil is given by the formula: Weight = Volume * Specific Gravity.

Given that the specific gravity of the oil is 0.85, we can calculate the weight of the oil as follows:

Weight of the oil = 523.6 cm^3 * 0.85 ≈ 445.06 g

Now, we need to determine the dimensions of the cubic steel.

The weight of the steel is equivalent to the weight of the oil, so we need to find the volume of the steel that has the same weight. The weight of the steel is given by the formula: Weight = Volume * Specific Gravity.

Given that the specific gravity of the steel is 7.1, we can calculate the volume of the steel as follows:

Volume of the steel = Weight of the oil / Specific Gravity of the steel
Volume of the steel = 445.06 g / 7.1 ≈ 62.66 cm^3

Since the volume of a cube is given by the formula: V = s^3, where s is the length of each side of the cube, we can find the dimension of the cubic steel by taking the cube root of the volume. Therefore:

s^3 = 62.66 cm^3
s ≈ ∛(62.66) ≈ 3.99 cm

Hence, the dimension of the cubic steel that has the same weight as the oil is approximately 3.99 cm on each side.