Geometry Answers

1. A factory’s pressure tank rests on the upper base of a vertical pipe whose inside diameter is 1 1/2 ft and whose length is 40 ft. The tank is a vertical cylinder surmounted by a cone, and it has a hemispherical base. If the altitudes of the cylinder and the cone are respectively 6 ft and 3 ft and all three parts of the tank have an inside diameter of 6 ft, find the volume of water in the tank and pipe when full.

2. A right circular cylinder whose diameter is 4 cm is cut from a right circular cone of height is 14 cm and radius 7 cm. What is the volume of the right circular cylinder?

1. Water is flowing out of a conical funnel through its apex at a rate of 12 cubic inches per minute. If the tunnel is initially full, how long will it take for it to be one-third full? What is the height of the water level? Assume the radius to be 6 inches and the altitude of the cone to be 15 inches.

2. Two similar cones have volumes 81 pi over 2 inches cube and the slant height of the bigger cone is 7.5 inches. Find the integer solution to the height of the smaller cone.

3. If the slant height of the cone is 16 inches and the total area is 120 pi square inches, find the height of the cone.

4. What is the height if a right circular cone having a slant height of 6 square root of 10 units and a base radius of 6 units?

5. Find the ratio of the slant height to the radius of a right circular cone in which the volume and lateral area are numerically equal. Assume the altitude of the cone to be 9 units.

1. The lateral edge of a regular hexagonal pyramid is two times the length of the base edge. If the apothem of the base is 8 cm, find the altitude and the volume of a cone inscribed in the pyramid.

2. If the diameter of the base remains constant, by what factor should the altitude be multiplied to produce a cone with twice volume as the original.

3.If the altitude of a cone remains constant, by what factor should the diameter be multiplied in order to construct a cone with a volume that is triple the original.

Find the radius and diameter of a circle with the following circumferences. If you need to, use 3 for π.

C = 30 inches
C = 37.5 inches
C = 50π cm
C = 26π cm
C = 18.6 ft

A tank, open at the top is made of sheet iron 1 in. thick. The internal dimensions of the tank are 4 ft., 8 in. long; 3 ft. wide 6 in. wide; 4 ft. 4 in. deep. Find the weight of the tank when empty, and find the weight when full of salt water.

Find the volume of a regular hexahedron if one of the diagonals of its faces is 8 square root 2 inches.

A cork in the shape of a cylinder has a radius of 2cm a height of 5cm and weighs 2.5 grams. What is the volume of the cork? What is the corks density in grams per cubic centimeter? That is how many grams of cork are there per cubic centimeter?

the peak of the mountain is 9,000 meters from the base. To climb up the side of the mountain it is 12,000 meters. how many meters deep is the radius of the mountain at its base?

A solid object consists of a 4*4*4 cube with a 3*3*3 cube sticking out. Three corners of the 3*3*3 cube lie on the edges of the 4*4*4 cube.The same distance along each edge. What is the combined volume of this object?

BACKSTORY: I need to collect 500 plant samples for strontium analysis. The samples are randomly distributed across a circular area with a radius of 300 kilometers. I have to do this in 30 days, so I want to be methodical.

REQUEST: Divide the circle into 30 regions of equal area using lines and/or arcs, NONE OF WHICH pass through the center of the circle. One wrinkle: I'd like each of the regions to have the highest compactness possible. That is, I'd like the average ratio of the area of the regions to the area of a circle having the same perimeter to be as close to 1:1 as possible.

DESIRED RESULT: An explanation of how to do this myself is good; a pdf of the solution is better!