Find the Area of the Part of Hyperbolic Paraboloid $z = y ^ { 2 } - x ^ { 2 }$

question 52

Multiple Choice

Find the area of the part of hyperbolic paraboloid $z = y ^ { 2 } - x ^ { 2 }$ that lies between the cylinders $x ^ { 2 } + y ^ { 2 } = 1$ and $x ^ { 2 } + y ^ { 2 } = 36$ .

• A) \(( 1297 \sqrt { 1297 } + 5 \sqrt { 5 } ) \pi\)
• B) \(( 1297 \sqrt { 1297 } - 6 \sqrt { 5 } ) \pi\)
• C) \(\frac { 1 } { 9 } ( 1297 \sqrt { 1297 } - 6 \sqrt { 5 } ) \pi\)
• D) \(\frac { 1 } { 9 } ( 1297 \sqrt { 1297 } - 5 \sqrt { 5 } )\)
• E) \(\frac { 1 } { 9 } ( 1297 \sqrt { 1297 } - 5 \sqrt { 5 } ) \pi\)

---

Definitions:

Value of Money

The purchasing power of money, which can vary based on inflation or deflation, affecting how much goods and services can be bought.

Inflation Rate

Over time, the increment in the price level percentage for goods and services in an economy.

Tax Rate

The proportion of income that is required to be paid as tax by a person or a company.

Real Interest Rate

The real interest rate is the interest rate adjusted for inflation, representing the true cost of borrowing and the true yield for savers.