Volumes of solids: problems
Find the volume of a part from the rise of the water, the radius of a melted ball and the volume of a solid made by turning a triangle or a trapezium. Keep π in the answer.
- Ukraine: grade 11
- Russia: grade 11
Guide
In the Ukrainian programme this is Grade 11 geometry: §22 "Volume of a solid" and §23 "Volumes of solids of revolution. Area of a sphere" (problems 4, 7, 14, 35, 43-45). Formulas: V = πr2h (cylinder), V = 13πr2h (cone), V = 43πR3 (ball).
A solid of revolution is made by turning a plane figure about a line. A rectangle turned about a side gives a cylinder; a right triangle turned about a leg gives a cone (the leg on the axis is the height h, the other leg is the radius r, the hypotenuse is the slant). In a problem like this, first think which solid appears and which length is the radius and which the height.
The textbook leaves π in the answer, for example 98π cm³. Type the number before π in the box; π has its own button. All lengths are in centimetres.