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
41 of 42 questions match · page 2 of 3. 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
The base radius of a right circular cone is 4 m while its slant height is 10 m. What is the lateral surface area?
A124.8 sq. m
B128.6 sq. m
C226.8 sq. m
D125.7 sq. m
The base radius of a right circular cone is 4 m while its slant height is 10 m. What is the lateral surface area?
A127.5 sq. m
B125.7 sq. m
C139.5 sq. m
D135.9 sq. m
A tank in an ice plant is to contain 3,000 liters of brine. It is constructed to be 4 m long and 1.5 m wide. Find the height of the tank.
A0.3
B0.4
C0.5
D0.6
The volume of a cube becomes three times when its edge is increased by 1 inch. What is the edge of the cube?
A2.62
B2.26
C3.26
D3.62
Find the volume of a cube if its total surface area is 54 sq. cm.
A21 cu. cm
B30 cu. cm
C27 cu. cm
D54 cu. cm
The lateral area of a right circular cylinder is 77 sq. cm and its volume is 231 cu. cm. Find its radius.
A4 cm
B5 cm
C6 cm
D7 cm
A cylinder of radius 3 is cut through the center of the base by a plane making an angle of 45 degrees with the base. Find the volume cut off.
A15
B16
C17
D18
The volume of a cube becomes three times when its edge is increased by 1 inch. What is the edge of the cube?
A2.62
B2.26
C3.26
D3.62
Each side of the base of a square pyramid is 10 inches. The slant height of this pyramid measures 12 in. What is the area, in square inches, of the base of the pyramid?
A100
B144
C120
D240
The longest diagonal of a cube is 6 cm. The total area of the cube is
A\(32\sqrt{2}\) sq. cm
B72 sq. cm
C\(24\sqrt{2}\) sq. cm
D36 sq. cm