Ahmed found the volume of a cone having both a height and a diameter of 6 centimeters. His work is shown below.

Step 1 Find the radius.
radius = StartFraction 6 Over 2 EndFraction = 3 centimeters
Step 2 Find the area of the base.
Area of base = Pi (3) squared = 9 pi centimeters squared
Step 3 Multiply the area of the base by the height.
9 pi times 6 = 54 centimeters cubed
Step 4 Divide 54 by 3 to find the volume of the cone.
Volume of the cone = StartFraction 54 Over 3 EndFraction = 18 centimeters cubed

What was Ahmed’s first error?
In Step 1, the radius should be found by multiplying the diameter by 2.
In Step 2, the formula 2 pi r should be used to find the area of the circle.
In Step 3, the resulting area should be in terms of pi.
In Step 4, the units of the resulting volume should be Centimeters squared.

In Step 3, the resulting area should be in terms of pi.

Step-by-step explanation:

The question here involves a cone shape. The volume of a cone can be calculated using the formula: 1/3 πr^2h

According to the question, the diameter (d) and height (h) are 6cm respectively. Ahmed calculated the volume of this cone but made an error in step 3. Using the same way Ahmed solved it, the correct step by step calculation is as follows:

Step 1: Find the radius

Radius (r) = diameter/2

= 6/2 = 3cm

Step 2: Find the area of the base.

The base of a cone is a circle. The area of a circle is calculated using, πr^2 where r is radius and π is pie

Hence, Area of base = π × 3^2

Area = π × 3 × 3

Area = 9π centimeter square (cm^2)

Step 3: Multiply the area of the base by the height.

Area of base = 9π cm^2, height of cone = 6cm

Hence, we have; 9π × 6

= 54π centimeters cube (cm^3).

Step 4: Divide 54π by 3 to find the volume of the cone.

That is, 54π ÷ 3 = 18π

Hence, the volume of the cone is 18π centimeters cube (cm^3).

Therefore, Ahmed's first error was in step 3 where he failed to express 54 in terms of pie(π).