The volume of the frustum of a regular triangular pyramid is \(135\) cu. m. The lower base is an equilateral triangle with an edge of \(9\) m. The upper base is \(8\) m above the lower base. What is the upper base edge in meters?
A2
B3
C4
D5
Mathematics · Question Bank
Solid Geometry
6 of 42 questions match. Answer in your head first, then check the solution.
In a portion of an electrical railway cutting, the areas of cross section taken every \(50\) m are \(2556\), \(2619\), \(2700\), \(2610\) and \(2484\) sq. m. Find its volume.
A\(522{,}600 \text{ m}^3\)
B\(520{,}500 \text{ m}^3\)
C\(540{,}600 \text{ m}^3\)
D\(534{,}200 \text{ m}^3\)
Two vertical conical tanks are joined at the vertices by a pipe. Initially the bigger tank is full of water. The pipe valve is open to allow the water to flow to the smaller tank until it is full. At this moment, how deep is the water in the bigger tank? The bigger tank has a diameter of \(6\) ft and a height of \(10\) ft, the smaller tank has a diameter of \(6\) ft and a height of \(8\) feet. Neglect the volume of water in the pipeline.
A\(\sqrt[3]{200}\)
B\(\sqrt[3]{50}\)
C\(\sqrt[3]{25}\)
D\(\sqrt[4]{50}\)
A mixture compound of equal parts of two liquids, one white and the other black, was placed in a hemispherical bowl. The total depth of the two liquids is \(6\) inches. After standing for a short time, the mixture separated, the white liquid settling below the black. If the thickness of the segment of the black liquid is \(2\) inches, find the radius of the bowl in inches.
A7.33
B7.53
C7.73
D7.93
An ice cream cone is filled with ice cream and a surmounted ice cream in the form of a hemisphere on top of the cone. If the hemispherical surface is equal to the lateral area of the cone, find the total volume (in cubic inches) of ice cream if the radius of the hemisphere is \(1\) inch and assuming the diameter of hemisphere is equal to the diameter of the cone.
A3.45
B3.91
C4.12
D4.25
A cubical container that measures \(2\) inches on a side is tightly packed with \(8\) marbles and is filled with water. All \(8\) marbles are in contact with the walls of the container and the adjacent marbles. All of the marbles are of the same size. What is the volume of water in the container?
A\(0.38 \text{ in}^3\)
B\(2.5 \text{ in}^3\)
C\(3.8 \text{ in}^3\)
D\(4.2 \text{ in}^3\)