Geometry Answers

If measure angle 1 equals 3x + 15 and measure angle 2 equals 6x + 3 find x

given ab and bc are tangents of d and the acd=15 what is the measure of abc?

4)If two vectors are given as A= -11i+2j (m) and B= 3i+3j (m), determine the resultant vector R=3A-B/2, and also find its magnitude R and direction?

how many decimeter are there in 15 centimeter

1. The frustum of a right circular cone has a slant height of 9 ft. and the radii of the bases are 5 ft. and 7 ft.

a. Find the lateral area and total area of the frustum.
b. What is the altitude of this frustum?
c. Find the altitude of the cone that was removed to leave this frustum.
d. What is the volume of the entire cone?

2.Consider the right pentagon pyramid. The sides of the upper and lower bases of the frustum are 4 and 10 inches, respectively, and the altitude of a lateral face is 6 inches. Find:

a. Lateral area of the frustum
b. Total area of the frustum
c. Volume of the frustum
d. Volume of the entire pyramid.

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.