Question

A solid has cross sections that are squares. The side lengths of the square cross sections are equal to x^2, where 0≤x≤1. Suppose the solid is divided by planes perpendicular to the x-axis into five pieces of equal thickness, and each slice is replaced by a square prism of thickness 0.2, and side lengths equal to xi^2, where xi ∈{0.1,0.3,0.5,0.7,0.9}. Which of the following best represents the volume of this object that approximates the original solid?

A. 0.113

B. 0.193

C. 0.313

D. 0.330

E. 0.440

Which of the following best represents the exact volume of the original solid?

A. 0.143

B. 0.167

C. 0.200

D. 0.333

E. 0.500

Answer 1

A) D- 0.330

B) D- 0.333

Explanation:

Part A

0.2 × (0.1² + 0.3² + 0.5² + 0.7² + 0.9²)

= 0.330

B) integrate x²

x³/3

Limits 0 to 1

1/3 - 0

1/3

0.333