The frustum of a right circular cone has the diameter of a base 10 cm, of top…

Solution:

Step-by-step reasoning to find the slant height of the frustum.

• Find the radii from the given diameters: radius of the base = 10/2 = 5 cm; radius of the top = 6/2 = 3 cm.

• The horizontal leg of the right triangle (along the sloping side) is the difference of the radii: 5 − 3 = 2 cm.

• The vertical leg is the height of the frustum: 5 cm.

• Apply the Pythagorean theorem to these two legs to get the slant height l:

l = √[(difference of radii)^2 + (height)^2] = √(2^2 + 5^2) = √(4 + 25) = √29.

Therefore the slant height of the frustum is √29 cm (approximately 5.385 cm).