The cylinder and cone have a common base and a common height. Calculate the volume of the cylinder

The cylinder and cone have a common base and a common height. Calculate the volume of the cylinder if the volume of the cone is 17.

1) The cylinder and the cone have:

common base, therefore the areas of their bases are equal: Sosn. c. = S main. to. = S;

total height – Hц = Hк = H.

2) Recall the formulas for calculating the volumes of a cylinder (Vc) and a cone (Vc):

Vts = Sbn. c. * Hts = S * H;

Vk = 1/3 * Sb. K. * Hk = 1/3 * S * H.

3) Since S * H = Vts, then

Vk = 1/3 * Vts;

Vk = Vts / 3.

4) Then the volume of a given cylinder can be calculated by the formula:

Vc = Vk * 3, that is, increase the known volume of the cone by 3 times.

Vts = 17 * 3;

Vts = 51.

Answer: the volume of the cylinder is 51.