A solid cylinder has an area of 10cm2 and a height of 1.0 m. The cylinder is composed of two different materials with mass densities of 2000 kg/m3 and 1500 kg/m3. If each of the two materials occupies an equal volume, what is the mass of the cylinder?

Question 3 options:
A) 3.5kg

B) 2.5kg

C) 25kg

D) 1.75kg

1m = 100cm.

V = 10cm^2 * 100cm = 1000cm^3.
1000cm^3 = 1*10^-3 m^3.

1*10^-3m^3/2 = 0.5*10^-3m^3 = 5*10^-4.

Mass = (2000kg/m^3)*5*10^-4m^3 +
(1500kg/m^3)*5*10^-4 = 3500*5*10^-4 =
1.75kg.

To solve this problem, we need to find the volume of each material and then calculate the total mass of the cylinder.

First, let's find the volume of the cylinder. The volume of a cylinder is given by the formula:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

Since the area of the cylinder is given as 10 cm^2, we can find the radius using the formula:

A = πr^2

Solving for r, we get:

r = √(A/π) = √(10/π) cm

Next, we need to convert the height of the cylinder to the same units as the radius. Since the radius is in cm, we need to convert the height to cm as well.

1 m = 100 cm

Now, let's find the volume of the cylinder using the formula:

V = πr^2h

V = π(√(10/π))^2 * 100 cm^3

V = 1000 cm^3

Since each material occupies an equal volume, each material occupies half of the total volume of the cylinder.

The mass of each material is given by:

m1 = ρ1 * V/2

m2 = ρ2 * V/2

where m1 and m2 are the masses of the two materials, ρ1 and ρ2 are the mass densities of the two materials, and V is the volume of the cylinder.

Now, let's calculate the masses of the two materials.

m1 = 2000 kg/m^3 * 1000 cm^3 / 2 = 1000000 kg.cm^3

m2 = 1500 kg/m^3 * 1000 cm^3 / 2 = 750000 kg.cm^3

Finally, let's calculate the total mass of the cylinder by summing up the masses of the two materials.

Total mass = m1 + m2 = 1000000 kg.cm^3 + 750000 kg.cm^3 = 1750000 kg.cm^3

Since the answer choices are given in kg, we need to convert kg.cm^3 to kg.

1 kg.cm^3 = 1 * 10^-6 kg

Total mass = 1750000 kg.cm^3 * 1 * 10^-6 kg = 1.75 kg

Therefore, the correct answer is D) 1.75 kg.