David as asked to find the volume of the shape below. Use 3.14 for π.

Question

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

Answer 1

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.

Answer 2

can you explain the steps in a paragraph please

Answer 3

Certainly! To find the volume of the given shape, we first calculate the volume of the cylinder by using the formula V = π * r^2 * h, where r is the radius and h is the height. Substituting the values provided (r = 7 cm, h = 10 cm), we find the volume of the cylinder to be 1538.6 cm^3. Next, we calculate the volume of the cone using the formula V = 1/3 * π * r^2 * h, where r is the radius, h is the height, and l is the slant height. Substituting the values (r = 7 cm, h = 10 cm), we find the volume of the cone to be 1617.3 cm^3. Finally, we add the volumes of the cylinder and cone together to get the total volume of the shape, which is 3155.9 cm^3.