Solve the problem.
-A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 31 feet and the distance across the top of the mirror is 66 inches, how deep is the mirror in the center?
A) $\frac { 121 } { 1984 }$ in.

B) $\frac { 363 } { 496 }$ in.

C) $\frac { 961 } { 132 }$ in.

D) $\frac { 1089 } { 124 } \mathrm { in }$.

Question

Solve the problem.
-A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 31 feet and the distance across the top of the mirror is 66 inches, how deep is the mirror in the center? 
A) $\frac { 121 } { 1984 }$ in.

B) $\frac { 363 } { 496 }$ in.

C) $\frac { 961 } { 132 }$ in.

D) $\frac { 1089 } { 124 } \mathrm { in }$.

Quizplus · Accepted Answer

The depth of the mirror can be found using the formula for a paraboloid of revolution, $y = \frac{1}{4f}(x^2)$, where $f$ is the focal length and $x$ is the radius of the mirror. The focal length is 31 feet, which is 372 inches. The diameter of the mirror is 66 inches, so the radius is 33 inches. Plugging these values into the formula gives $y = \frac{1}{4(372)}(33)^2 = \frac{1089}{1488} = \frac{363}{496}$ inches.

Solve the Problem 1211984\frac { 121 } { 1984 }1984121​ In B)

Solve the Problem $\frac { 121 } { 1984 }$ In

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