SOLUTION: A square with side length 6 inches is revolved about a diagonal as an axis. Find the volume of the solid created by this revolution.

Question 134109: A square with side length 6 inches is revolved about a diagonal as an axis. Find the volume of the solid created by this revolution.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The solid figure would be two right circular cones, base to base. The pertinent dimensions of one of the cones, namely the radius of the base and the height of the cone, would both measure one-half the measure of the diagonal of the square.

Since the square has a side of 6, the diagonal measures , therefore half of the diagonal would measure .

The formula for the volume of a right circular cone in terms of the height and the radius of the base is: and since there are two such cones, we need to multiply this volume by 2, hence our total volume is given by:

RELATED QUESTIONS
The legs of a right triangle are 4ft. And 3ft. Find the lateral and the volume of the... (answered by Fombitz)

the legs of a right triangle are 4ft and 3ft. Find the lateral area and the volume of... (answered by Alan3354)

Please help me with this problem: Let R be the region bounded by the y axis and the... (answered by robertb)

A square of side 8cm is rotated around about its diagonal. Find the exact volume of the... (answered by ikleyn)

A 3 by 4 inches rectangle is revolved about its shorter side to generate a right circular (answered by ankor@dixie-net.com)

a triangle has sides that measure 6cm, 8cm, and 10cm. find the exact volume of the solid... (answered by ikleyn)

a triangle has sides that measure 6cm, 8cm, and 10cm. find the exact volume the solid of... (answered by ikleyn)

Find the volume of the solid formed when a circular sector of radius 6 cm and angle of... (answered by Alan3354)

Please help me with this problem: Let R be the region bounded by the x axis and the... (answered by Natolino1983)