# geometry

Suppose you have an equilateral triangle. The area of the triangle is exactly 1200 square centimetres. Now suppose you have twenty of those triangles. It's possible to assemble those twenty triangles into a closed three-dimensional shape, a regular polyhedron.

What would be the volume, in cubic centimetres, of the largest sphere that could fit inside the shape?

1. 👍
2. 👎
3. 👁
1. Please stop cheating at neopets!

1. 👍
2. 👎
2. The formula that you need for the radius of the inscribed sphere can be found in the link below, but deriving it would be rather difficult:

http://en.wikipedia.org/wiki/Icosahedron

Once you have the radius, compute the sphere volume in the usual way.

The Wikipedia reference gives the sphere radius in terms of the triangle side length, a. In your case, the side length is
a = [4/sqrt3 * A]^1/2 = 52.643 cm

1. 👍
2. 👎

## Similar Questions

1. ### Geometry

Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC. a) Draw a triangle ABC and then sketch the remainder of the figure. It will help if

2. ### math

(please explain with brief explanation) The sides of an equilateral triangle are shortened by 12 units,13 units and 14 units respectively and a right angled triangle is formed.Find the side of the equilateral triangle.

3. ### Math

Can someone please check to see if I answered these true and false statements correctly? Thank you! 1. A triangle can have two right angles. (TRUE??) 2. An equilateral triangle is also an acute. (TRUE??) 3. A right triangle can

4. ### math

a) What is the area of the tri-angle determined by the lines y= − 1/ 2x + 5,y =6x and they-axis? (b) If b > 0 and m < 0, then the line y = mx +b cuts off a triangle from the first quadrant. Express the area of that tri-angle in

1. ### Algebra 2

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Find the sum of a finite geometric series. The sides of an equilateral triangle measure 16 inches. The midpoints of the

2. ### Math

A square has an area of 27 square units. If the perimeter of the square is equal to the perimeter of an equilateral triangle, find the area of the equilateral triangle.

Which of the statements is ALWAYS TRUE? A-A right triangle is a scalene triangle. B-An equilateral triangle is an isosceles triangle. C-An isosceles triangle is an obtuse triangle. D-A right triangle is an acute triangle. I got

4. ### Geometry

An equilateral triangle has a perimeter of 120 inches. What is the area of the triangle? Express your answer in simplest radical form.

1. ### Maths

Here is a right- angled triangle. |\ | \ x | \ |___\ x - 2 All measurements are in centimetres. The area if the triangle is 2.5cm^2. Find the perimeter of the triangle. Key values: Equation for area: ? - __(___) = ? ? Quadratic

2. ### mathematics

A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 5 inches long, and the height of the equilateral triangle is 4.3 inches. The pyramid's slant height is 5 inches.

3. ### Math, Geometry

A square and an equilateral triangle have equal perimeters. The area of the triangle is 2\sqrt {3} square inches. What is the number of inches in the length of the diagonal of the square? Please give me a full clear explanation

4. ### calculus

a wire 60cm long is to be cut into two pieces, one of which is to be bent into the shape of a square and the other of which is to be bent into an equilateral triangle. find how the wire should be cut so that the combined area of