Solve the Problem $1 \mathrm {~cm} ^ { 2 }$ to Do This, You Need to Know How Much

Multiple Choice

Solve the problem.
-You are asked to make some circular cylinders, each with a cross-sectional area of $1 \mathrm {~cm} ^ { 2 }$ . To do this, you need to know how much deviation from the ideal cylinder diameter of $x _ { 0 } = 1.99 \mathrm {~cm}$ you can allow and still have the area come within $0.1 \mathrm {~cm} ^ { 2 }$ of the required $1 \mathrm {~cm} ^ { 2 }$ . To find out, let $A = \pi \left( \frac { x } { 2 } \right) ^ { 2 }$ and look for the interval in which you must hold $x$ to make $| A - 1 | < 0.1$ . What interval do you find?

A) (1.8974, 2.0976)
B) (1.0705, 1.1835)
C) (0.7569, 0.8368)
D) (0.5642, 0.5642)