David as asked to find the volume of the shape below. Use 3.14 for π.
Identify David's error and show all steps to arrive to the correct answer.
Math
David's error appears to be not considering the cylinder and the cone separately and adding their volumes together at the end, instead he used the total height for both shapes.
Let's first calculate the volume of the cylinder:
Given:
Radius (r) = 7 cm
Height (h) = 10 cm
Volume of a cylinder = π * r^2 * h
Volume = 3.14 * 7^2 * 10
Volume = 3.14 * 49 * 10
Volume = 1538.6 cm^3
Now, let's calculate the volume of the cone:
Radius (r) = 7 cm
Height (h) = 10 cm
Slant height (l) = 13 cm
Volume of a cone = 1/3 * π * r^2 * h
Volume = 1/3 * 3.14 * 7^2 * 10
Volume = 1/3 * 3.14 * 49 * 10
Volume = 1617.3 cm^3
Therefore, the correct answer for the total volume of the shape is 1538.6 cm^3 (cylinder) + 1617.3 cm^3 (cone) = 3155.9 cm^3.