Geometry Answers

Let AK, BL, CN be angle bisectors of triangle ABC, and they intersect at point I. It is known that the ratios of areas of triangles ANL , BKN and CLK to the area of triangle ABC are equal to (7/39), (9/65) and (7/15) respectively. Find the ratio of IK:AI

A right circular cone is inscribed in a cube having a diagonal which
measures 20 square root of 3 cm.

1. What is the altitude of the cone?

A monument is a stone structure in the form of a frustum of a regular square pyramid whose height is 50m and whose base edges are 4.5m and 10m respectively. Through the center of the monument is a circular opening 3m in diameter at the top and 6m in diameter at the bottom. Refer to figure 1.

8. What is the slant height of the opening?
9. What is the lateral surface area of the opening?
10. Find the volume of stone in the monument.

The volume of a frustum of a right circular cone is 52π cm3. Its altitude is 3cm and the measure of its lower radius is three times the measure of its
upper radius.

5. What is the radius of the upper base?
6. What is the slant height of the frustum?
7. Find the lateral area of the frustum.

A right circular cone is inscribed in a cube having a diagonal which
measures 20 square root of 3 cm.

3. What is the surface area of the cone?
4. What is the volume of the space between the cone and the cube?

An inverted regular square pyramid has an altitude of 12m and with top
edge of 3m is fully–filled with water.

6. How much water is to be removed so that water is 7m deep?

An inverted regular square pyramid has an altitude of 12m and with top edge of 3m is fully–filled with water What is the volume of the water in m3? A portion of water is to be removed so that water will be 7m deep.

A right circular cone is inscribed in a cube having a diagonal which
measures 20√3 cm.
Altitude of the cone = 20 cm
Volume of the cone = 2094.4 cubic centimeter
Surface Area of the cone = 942.5 cm squared
1. What is the volume of the space between the cone and the cube?

Line l touches the circle ω at point K. Points A and B are chosen on ω in such a way that they are situated on opposite sides with respect to the diameter of ω that passes through point K. Find the area of triangle AKB if the distances from points A and B to line l are equal to 7 and 11 respectively, and AK=13. Round the answer to the closest integer.