Solid Geometry
3D shapes—prisms, pyramids, cylinders, cones, spheres—surface area, volume, mensuration.
Solved Problems
TopicsMensuration of Plane Figures
Cube
A vegetable bin built in the form of a cube with an edge of \(6 ~ft\) is divided by a vertical partition which passes through two diagonally opposite edges. Find the lateral surface of either compartment.Find the volume and total area of the largest cube of wood that can be cut from a log of circular cross-section whose radius is 12.7 inches.If a cube has an edge equal to the diagonal of another cube, what is the ratio of their volumes?How much material was used in the manufacture if 24 000 celluloid dice, if each die has an edge of 0.25 inch?
Rectangular Parallelepiped
The edges of a trunk are 3ft, 4ft, 6ft. and a second trunk is twice as long; the other edges are 3ft, 4ft. How do their volumes compare?A tank open at the top, is made of sheet of iron 1 in thick. The internal dimensions of the tank are 4ft 8 in long; 3ft 6 in wide; 4 ft 4 in deep. Find the weight of the tank when empty, and find the weight when full of salt water. A solid concrete porch consists of 3 steps and a landing. The steps have a thread of 11 in arise of 7 in and a length of 7 ft.; the landing is 6 ft by 7ft. How much materials was used in its construction?How many cubic yards of material are needed for the foundation of a barn 40 ft by 80 ft, if the foundation is 2 ft thick and 12 ft high?
Prism
A trench is 180 ft. long and 12 ft. deep, 7 ft. wide at the top and 4ft. at the bottom. How many cubic yards of earth have been removed?One part of a quartz crystal is a hexagonal prism with a right section of 1.29 sq. in., an edge of 2.31 in, and a base of 1.41 sq. in. Find the altitude of the prism.
Tags:
solid geometry
mensuration
surface area
volume
prism
pyramid
cylinder
cone
sphere