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    Solid Geometry

    Solved Problems | Topics

    Cone
    ✔A cone axis is 30 cm which inclined at 60 o from the horizontal and has a base diameter of 20 cm. What is the volume of cone in cubic centimeters?
    Mensuration of Plane Figures
    ✔Find the area of the rectilinear figure shown, if it is the difference between two isosceles trapezoids whose corresponding sides are parallel
    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.
    Frustum
    ✔A water tank has a cylindrical shape with a diameter of 2 m and a perpendicular height of 3 m. Since it was already old and leaking, it is to be replaced by another tank of the same capacity but in the form of a frustum of a cone. The diameters of the ends of the frustum are designed to be 1 m and 2

    Tags: Solid Geometry, solid geometry formulas, solid geometry definition, solid geometry answers, solid geometry applications, Geometry Formulas, Mensuration, Volume of solids

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