The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve $z = \frac { 1 } { 4 } y ^ { 2 } + 1 , ( 0 \leq y \leq 4 ) \text { in the } y z - \text { plane about }$ the z-axis. Find an equation for the surface of revolution.
A) $x ^ { 2 } + y ^ { 2 } - 4 z + 4 = 0$
B) $x ^ { 2 } - y ^ { 2 } - 4 z + 4 = 0$
C) $x ^ { 2 } + y ^ { 2 } + 4 z - 4 = 0$
D) $4 x ^ { 2 } + y ^ { 2 } + 4 z ^ { 2 } - 4 = 0$
E) $4 x ^ { 2 } - y ^ { 2 } - 4 z ^ { 2 } - 4 = 0$

Question

The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve $z = \frac { 1 } { 4 } y ^ { 2 } + 1 , ( 0 \leq y \leq 4 ) \text { in the } y z - \text { plane about }$ the z-axis. Find an equation for the surface of revolution. 
A) $x ^ { 2 } + y ^ { 2 } - 4 z + 4 = 0$
B) $x ^ { 2 } - y ^ { 2 } - 4 z + 4 = 0$
C) $x ^ { 2 } + y ^ { 2 } + 4 z - 4 = 0$
D) $4 x ^ { 2 } + y ^ { 2 } + 4 z ^ { 2 } - 4 = 0$
E) $4 x ^ { 2 } - y ^ { 2 } - 4 z ^ { 2 } - 4 = 0$

Quizplus · Accepted Answer

The equation of the surface of revolution is obtained by replacing $y^2$ with $x^2 + y^2$ in the given curve equation $z = \frac{1}{4}y^2 + 1$, resulting in $z = \frac{1}{4}(x^2 + y^2) + 1$. Rearranging this equation gives $x^2 + y^2 - 4z + 4 = 0$.

The Top of a Rubber Bushing Designed to Absorb Vibrations z=14y2+1,(0≤y≤4) in the yz− plane about z = \frac { 1 } { 4 } y ^ { 2 } + 1 , ( 0 \leq y \leq 4 ) \text { in the } y z - \text { plane about }z=41​y2+1,(0≤y≤4) in the yz− plane about

The Top of a Rubber Bushing Designed to Absorb Vibrations $z = \frac { 1 } { 4 } y ^ { 2 } + 1 , ( 0 \leq y \leq 4 ) \text { in the } y z - \text { plane about }$