A circular cylinder is circumscribed about a right prism having a square base one meter on an edge. The volume of the cylinder is \(6.283\) cu.m. Find its altitude in meters.
A4.00
B3.75
C3.50
D3.25
Mathematics · Question Bank
Solid Geometry
30 questions · page 2 of 2. Answer in your head first, then check the solution.
The bases of a right prism is a hexagon with one of each side equal to \(6\) cm. The bases are \(12\) cm apart. What is the volume of the right prism?
A\(1211.6 \text{ cm}^3\)
B\(2211.7 \text{ cm}^3\)
C\(1212.5 \text{ cm}^3\)
D\(1122.4 \text{ cm}^3\)
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\(\sqrt[4]{50}\)
The central angle of a spherical wedge is \(1\) radian. Find its volume if its radius is \(1\) unit.
A\(2/3\)
B\(1/2\)
C\(3/4\)
D\(2/5\)
A regular octahedron has an edge \(2\) m. Find its volume (in \(\text{m}^3\))
A3.77
B1.88
C3.22
D2.44
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
The volume of water in a spherical tank having a diameter of \(4\) m is \(5.236 \text{ m}^3\). Determine the depth of the water in the tank.
A1.0
B1.2
C1.4
D1.8
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\(4.2 \text{ in}^3\)
The corners of a cubical block touched the closed spherical shell that encloses it. The volume of the box is \(2744\) cubic cm. What volume in cubic centimeter inside the shell is not occupied by the block?
A2714.56
B3714.65
C4713.56
D4613.74