The cylinder is made of steel and has a base area of 10cm ^ 2. What area of warp should a granite cylinder have

The cylinder is made of steel and has a base area of 10cm ^ 2. What area of warp should a granite cylinder have the same height so that the pressure exerted by the cylinders on the table is the same. Density of granite 2600 kg \ m ^ 3

Sc = 10 cm2 = 0.001 m2.

hc = hg.

ρс = 7800 kg / m3.

ρg = 2600 kg / m3.

g = 10 N / kg.

Pc = Pg.

Sg -?

The pressure of the steel Pc and granite Pg cylinder on the table is expressed by the formulas: Pc = Nc / Sc, Pg = Ng / Sg, where Nc is the weight of the steel cylinder, Ng is the weight of the granite cylinder, Sc, Sg are the areas of the bases of the steel and granite cylinder.

We express the weight of the cylinders by the formulas: Nc = mc * g = ρc * Vc * g = ρc * Sc * hc * g, Ng = mg * g = ρg * Vg * g = ρg * Sg * hg * g.

Рс = ρc * Sc * hс * g / Sс = ρc * Sc * hс * g.

Pg = ρg * Sg * hg * g / Sg = ρg * Sg * hg * g.

ρc * Sc * hc * g = ρg * Sg * hg * g.

Sg = ρc * Sc * hc * g / ρg * hg * g = ρc * Sc / ρg.

Sg = 7800 kg / m3 * 0.001 m2 / 2600 kg / m3 = 0.003 m2.

Answer: a granite cylinder should have a base area Sg = 0.003 m2.