Find the area of the part of the cone $4 x ^ { 2 } + 4 y ^ { 2 } = z ^ { 2 }$ that is above the region in the first quadrant bounded by the line y = x and the parabola $y = x ^ { 2 }$ .
A) $\frac { 5 } { 6 }$

B) $\frac { 5 } { 3 }$
C)$\frac { 2 } { 3 }$
D)2
E) $\frac { \sqrt { 5 } } { 6 }$
F) $\frac { \sqrt { 5 } } { 3 }$

G) $\frac { \sqrt { 2 } } { 5 }$
H)6

Question

Find the area of the part of the cone $4 x ^ { 2 } + 4 y ^ { 2 } = z ^ { 2 }$ that is above the region in the first quadrant bounded by the line y = x and the parabola $y = x ^ { 2 }$ .
A) $\frac { 5 } { 6 }$

B) $\frac { 5 } { 3 }$ 
C)$\frac { 2 } { 3 }$
D)2
E) $\frac { \sqrt { 5 } } { 6 }$ 
F) $\frac { \sqrt { 5 } } { 3 }$ 
 
G) $\frac { \sqrt { 2 } } { 5 }$ 
H)6

Quizplus · Accepted Answer

The correct answer is E because the area of the part of the cone $4 x ^ { 2 } + 4 y ^ { 2 } = z ^ { 2 }$ that is above the region in the first quadrant bounded by the line y = x and the parabola $y = x ^ { 2 }$ is $\frac { \sqrt { 5 } } { 6 }$.

Find the Area of the Part of the Cone 4x2+4y2=z24 x ^ { 2 } + 4 y ^ { 2 } = z ^ { 2 }4x2+4y2=z2

Find the Area of the Part of the Cone $4 x ^ { 2 } + 4 y ^ { 2 } = z ^ { 2 }$