What is the diameter (in cm) of a solid right circular cylinder whose height is 6 cm and the area of the curved surface is five times the combined area of the two flat surfacesQuestion 6Answera.3b.1.2c.2.4d.0.9

The problem is asking for the diameter of a solid right circular cylinder given that the height is 6 cm and the area of the curved surface is five times the combined area of the two flat surfaces.

Step 1: Understand the formulae The area of the curved surface of a cylinder (A) is given by 2πrh, where r is the radius and h is the height. The combined area of the two flat surfaces (B) is given by 2πr^2.

Step 2: Set up the equation According to the problem, A = 5B. Substituting the formulae from step 1, we get 2πrh = 5 * 2πr^2.

Step 3: Simplify the equation The 2πr on both sides can be cancelled out, leaving us with h = 5r.

Step 4: Substitute the given values We know that h = 6 cm. Substituting this into the equation gives 6 = 5r.

Step 5: Solve for r Dividing both sides by 5 gives r = 6/5 = 1.2 cm.

Step 6: Find the diameter The diameter of a circle is twice the radius, so the diameter of the cylinder is 2 * 1.2 = 2.4 cm.

So, the answer is c. 2.4 cm.