Find an Equation for the Surface Obtained by Rotating the Parabola

question 59

Multiple Choice

Find an equation for the surface obtained by rotating the parabola $y = 3 x ^ { 2 }$ about the y-axis.

• A) \(y ^ { 2 } + 3 x ^ { 2 } = z\)
• B) \(z ^ { 2 } + 3 x ^ { 2 } = y\)
• C) \(z ^ { 2 } + 3 x ^ { 2 } + y ^ { 2 } = 1\)
• D) \(z ^ { 2 } - 3 x ^ { 2 } - y ^ { 2 } = 1\)
• E) \(z ^ { 2 } - 3 x ^ { 2 } = y\)

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Definitions:

Physical Properties

Characteristics of a substance that can be observed without changing its identity, such as color, density, and melting point.

Cognitive Development

The process by which individuals acquire and evolve their thinking abilities, including the development of logic and reasoning skills, throughout life.

Conservation Problem

Conservation problems refer to the difficulties or issues associated with preserving and managing natural resources and ecosystems in a sustainable manner.

Cognitive Development

Refers to the progression of thinking, problem solving, and information processing abilities from childhood through adolescence to adulthood.