Geometry Answers

The surface area of a sphere inscribed in a regular tetrahedron is 144pi centimeter squared.
1. What is the radius of the sphere?

2. What is the altitude of the tetrahedron?

3. If a sphere is inscribed in a cube of side 12cm, what is the volume of the sphere?

The base of a right prism is an equilateral triangle whose edges is 10cm each and its lateral edge is 80cm.
1. Find its volume in cm3.

2. Determine the total area of the prism in cm2.

Let ABC be a triangle such that AB= 5, AC= 8, and ∠BAC= 60◦. Let P be a point inside the triangle such that ∠APB = ∠BPC = ∠CPA. Lines BP and AC intersect at E, and lines CP and AB intersect at F. The circumcircles of triangles BPF and CPE intersect at points P and Q not equal P. Then QE + QF = m/n, where m and n are positive integers with gcd(m,n) = 1. Compute 100m+n.

PROBLEM 3. Find the radius of a cone of revolution of slant height 6 inches in which the total area is twice the lateral area.
FINAL ANSWER: _______________________________________

PROBLEM 2. A block of wood is in the form of a right circular cone. The altitude is 12 cm and the radius of the base is 5 cm. A cylindrical hole of 5 cm is bored completely through the solid, the axis of the hole coinciding with the axis of the cone. Find the amount of wood left after the hole is bored.
FINAL ANSWER: _______________________________________

PROBLEM 2. A pyramidal monument has an octagonal base, each side of which is 2 m. Each lateral edge of the pyramid is 3m. Find the total cost of painting the lateral surface of the monument at PhP 730.00 per square meter?
FINAL ANSWER: _______________________________________

a cylindrical silo has a hemispherical top. the cylinder has a height of 40 m and a base diameter of 12m.

b. the silo should be filled no more than 80% capacity. how much grain can be put in the silo>

c. a truck with a bin measuring 8 m by 4 m by 3.5m delivers grain. how many truckloads would fill a silo to its recommended capacity

a truck measuring 8m by 4m by 3.5m delivers grain to the farm. how many truckloads would fill the silo to its recommended capacity

A lampshade in form of a frustum of cone has height of 12cm upper and lower diameter of 10cm and 20cm respectively what area of material is required to cover the curved surface area

PROBLEM 4. In a frustum of right circular cone the altitude is 3 cm and the radii of the bases are 2 cm and 6 cm. Find the lengths of the slant height and altitude of the entire cone of which this frustum is a part.
FINAL ANSWER: ______________________________ ____________________________________