A trough has an open top 0.30 m by 6 m and closed vertical ends which are equilateral triangles 30 cm on each side. It is filled with water to half its depth. Find the volume of the water in cubic meters.

The volume of a regular tetrahedron of side 5 cm is:

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

A regular hexagonal pyramid whose base perimeter is 60 cm has an altitude of 30 cm, the volume of the pyramid is:

A frustum of a pyramid has an upper base 100 m by 10 m and a lower base of 80 m by 8 m. if the altitude of the frustum is 5 m, find its volume.

The altitude of the frustum of a regular rectangular pyramid is 5m the volume is 140 cu. m. and the upper base is 3m by 4m. What are the dimensions of the lower base in m?

The frustum of a regular triangular pyramid has equilateral triangles for its bases. The lower and upper base edges are 9 m and 3 m, respectively. If the volume is 118.2 cu. m.., how far apart are the base?

A cylindrical gasoline tank, lying horizontally, 0.90 m. in diameter and 3 m long is filled to a depth of 0.60 m. How many gallons of gasoline does it contain? Hint: One cubic meter = 265 gallons

A closed cylindrical tank is 8 feet long and 3 feet in diameter. When lying in a horizontal position, the water is 2 feet deep. If the tank is the vertical position, the depth of water in the tank is:

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 m. meter on an edge. The volume of the cylinder is 6.283 cu. m. Find its altitude in m.

If 23 cubic meters of water are poured into a conical vessel, it reaches a depth of 12 cm. how much water must be added so that the length reaches 18 cm.?

The height of a right circular base down is h. If it contains water to depth of 2h/3 the ratio of the volume of water to that of the cone is:

A right circular cone with an altitude of 9m is divided into two segments; one is a smaller circular cone having the same vertex with an altitude of 6m. Find the ratio of the volume of the two cones.

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 of its content in cc.

A right circular cone with an altitude of 8 cm is divided into two segments. One is a smaller circular cone having the same vertex with the volume equal to ¼ of the original cone. Find the altitude of the smaller cone.

The slant height of a right circular cone is 5m long. The base diameter is 6m. What is the lateral area in sq. m?

A right circular cone has a volume of 128π/3 cm3 and an altitude of 8 cm. The lateral area is:

The volume of a right circular cone is 36π. If its altitude is 3, find its radius.

A cone and hemisphere share base that is a semicircle with radius 3 and the cone is inscribed inside the hemisphere. Find the volume of the region outside the cone and inside the hemisphere.

A cone was formed by rolling a thin sheet of metal in the form of a sector of a circle 72 cm in diameter with a central angle of 210°. What is the volume of the cone in cc?

A cone was formed by rolling a thin sheet of metal in the form of a sector of a circle 72 cm in diameter with a central angle of 150°. Find the volume of the cone in cc.

A chemist’s measuring glass is conical in shape. If it is 8 cm deep and 3 cm across the mouth, find the distance on the slant edge between the markings for 1 cc and 2 cc.

The base areas of a frustum of a cone are 25 sq. cm. and 16 sq. cm, respectively. If its altitude is 6 cm, find its volume.

What is the surface area of a sphere whose volume is 36 cu. m?

If the surface area of a sphere is increased by 21%, its volume is increased by:

The surface area of the sphere is 4πr2. Find the percentage increase in its diameter when the surface area increases by 21%

Given two spheres whose combined volume is known to be 819 cu. m. if their radii are in the ratio 3:4, what is the volume of the smaller sphere?

How much will the surface area of a sphere be increased if its radius is increased by 5%?

The volume of a sphere is 904.78 cu. m. Find the volume of the spherical segment of height 4 m.

A sphere of radius r just fits into a cylindrical container of radius r and altitude 2r. Find the empty space in the cylinder.

If a solid steel ball is immersed in an eight cm. diameter cylinder, it displaces water to a depth of 2.25 cm. the radius of the ball is:

The diameter of two spheres is in the ratio 2:3. If the sum of their volumes is 1,260 cu. m., the volume of the larger sphere is:

A hemispherical bowl of radius 10 cm is filled with water to such a depth that the water surface area is equal to 75π cm2. The volume of water is:

A water tank is in the form of a spherical segment whose base radii are 4 m and 3 m and whose altitude is 6 m. The capacity of the tank in gallon is:

Find the volume of a spherical sector of altitude 3 cm. and radius 5 cm.

How far from the center of a sphere of a radius 10 cm should a plane be passed so that the ratio of the areas of two zones is 3:7?

A 2-m diameter spherical tank contains1396 liter of water. How many liters of water must be added for the water to reach a depth of 1.75 m?

Find the volume of a spherical segment of radius 10 m and the altitude 5 m.

Find the volume of a spherical wedge of radius 10 cm. and central angle 50°.

Determine the area of the zone of a sphere of radius 8 in. and altitude 12 in.

The corners of a cubical block touch the closed spherical shell that encloses it. The volume of the box is 2744 cc. What volume in cc, inside the shell is not occupied by the block?

A cubical container that measures 2 inches on each 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?

The volume of the water is a spherical tank is 1470.265 cm3. Determine the depth of water if the tank has a diameter of 30 cm.

A mixture compound from 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”. 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”, find the radius of the bowl in inches.

20.5 cubic meters of water is inside a spherical tank whose radius is 2 m. find the height of the water surface above the bottom of the tank, in m.

The volume of the sphere is 3π cu. m. The surface area of this sphere in sq. m. is:

Spherical balls 1.5 cm in diameter area packed in a box measuring 6 cm by 3 cm by 3 cm. If as many balls as possible are packed in the box, how much free space remains in the box?

A solid has a circular base of radius r. find the volume of the solid if every plane perpendicular to a given diameter is a square.

A solid has circular base of diameter 20 cm. Find the volume of the solid if every cutting plane perpendicular to the base along a given diameter is an equilateral triangle.

The volume generated by the circle by the circle x2 + y2 + 4x – 6y – 12 = 0 revolved about the line 2x – 3y – 12 = 0 is:

The volume generated by rotating the curve 9×2 + 4y2 = 36 about the line 4x + 3y = 20 is:

Find the volume generated by revolving the area bounded by the ellipse (y2/9) + (x2/4) = 1 about the line x = 3.

A square hole 2” x 2” is cut through a 6-inch diameter long along its diameter and perpendicular to its axis. Find the volume of wood that was removed.

Given an ellipse whose semi-major axis is 6 cm. and semi-minor axis is 3 cm. what is the volume generated if it is revolved about the minor axis?

A square area of edge “a” revolves about a line through one vertex, making an angle Ѳ with an edge and not crossing the square. Find the volume generated.

The area in the second quadrant of the circle x2 + y2 = 36 is revolved about the line y + 10 = 0. What is the volume generated?