A circular piece of cardboard with a diameter of 1 m will be made into a conical hat 40 cm high by cutting a sector off and joining the edges to form a cone. Determine the angle subtended by the sector removed.

What is the area in sq. me of the zone of a spherical segment having a volume of 1470.265 cu. m if the diameter of the sphere is 30 m?

If the edge of a cube is increased by 30%, by how much is the surface area increased?

A sphere having a diameter of 30 cm is cut into 2 segments. The altitude of the first segment is 6 cm. What is the ratio of the area of the second segment to that of the first?

Each side of a cube is increased by 1%. By what percent is the volume of the cube increased?

Given a sphere of a diameter, d. What is the percentage increase in its diameter when the surface area increases by 21%?

How many times does the volume of a sphere increases if the radius is doubled?

A circular having an altitude of 9 m is divided into 2 segments having the same vertex. If the smaller altitude is 6 m, find the ratio of the volume of the small cone to the big cone.

Find the volume of a cone to be constructed from a sector having a diameter of 72 cm and central angle of 210°.

A conical vessel has a height of 24 cm and a base diameter of 12 cm. It holds water to a depth of 18 cm above its vertex. Find the volume (in cm3) of its content.

Find the volume of a cone to be constructed from a sector having a diameter of 72 cm and a central angle of 150°.

The ratio of the volume to the lateral area of a right circular cone is 2:1. If the altitude is 15 cm, what is the ratio of the slant height to the radius?

A regular triangular pyramid has an altitude of 9 m and a volume of 187.06 cu. m. What is the base edge in meters?

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?

What is the volume of a frustum of a cone whose upper base is 15 cm in diameter and lower base 10 cm. in diameter with an altitude of 25 cm?

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.

Determine the volume of a right truncated triangular prism with the following definitions: Let the corners of the triangular base be defined by A, B and C. The length of AB = 10 ft., BC = 9 ft. and CA = 12 ft. The sides A, B and C are perpendicular to the triangular base and have the height of 8.6 ft., 7.1 ft. and 5.5 ft. respectively.

A circular cylinder with a volume of 6.54 cu. m is circumscribed about a right prism whose base is an equilateral triangle of side 1.25 m. What is the altitude of the cylinder in meters?

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.

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?

The central angle of a spherical wedge is 1 radian. Find its volume if its radius is 1 unit.

A regular octahedron has an edge of 2 m. Find its volume (in m3).

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.

The volume of water in a spherical tank having a diameter of 4 m is 5.236 m3. Determine the depth of the water in the tank.

An ice cream cone is filled with ice cream and 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.

A cubical container that measures 2 inches on a side is tightly packed with 8 marbles and is filled with water. All 8 marblesare 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?

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 centimeters inside the shell is not occupied by the block?

If the edge of a cube is doubled, which of the following is incorrect?

The volume of a cube is reduced by how much if all sides are halved?

Each side of a cube is increased by 1%. By what percent is the volume of the cube increased?

A rectangular bin 4 feet long, 3 feet wide, and 2 feet high is solidly packed with bricks whose dimensions are 8 in. by 4 in. by 2 in. The number of bricks in the bin is:

Find the total surface area of a cube of side 6 cm.

Find the approximate change in the volume of a cube of side x inches caused by increasing its side by 1%.

The space diagonal of a cube is 4√3 m. Find its volume.

A reservoir is shaped like a square prism. If the area of its base is 225 sq. cm, how many liters of water will it hold?

The space diagonal of a cube (the diagonal joining two non-coplanar vertices) is 6 m. The total surface area of the cube is:

Find the angle formed by the intersection of a face diagonal t the diagonal of a cube drawn from the same vertex.

The base edge of a regular hexagonal prism is 6 cm and its bases are 12 cm apart. Find its volume in cu. cm.

The base edge of a regular pentagonal prism is 6 cm and its bases are 12 cm apart. Find its volume in cu. cm.

The base of a right prism is a hexagon with one side 6 cm long. If the volume of the prism is 450 cc, how far apart are the bases?