Graph $x^{2} + y^{2} = 4$ in 3D looks like

Circle

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Cylinder

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Hemisphere

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Sphere

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Solution

The correct option is A Cylinder
The given curve is $x^{2} + y^{2} = 4$
So $x$ coordinate and y-coordinate are connected by $x^{2} + y^{2} = 4$
which is locus of a circle with radius $2$
But z-coordinate can be anything, so in three dimension the circle $x^{2} + y^{2} = 4$ will be
stretched which will be a cylinder with radius same as the radius of the circle .

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Similar questions

Q. The number of common tangents to the circles

x^{2} + y^{2} - 4 x - 6 y - 12 = 0

and

x^{2} + y^{2} + 6 x + 18 y + 26 = 0

Q. The number of distinct points common to the graphs of

x^{2} + y^{2} = 4

and

y^{2} = 4

The area of the circle x² + y² = 16 exterior to the parabola y² = 6x is

Q. The graph of the equation

x^{2} + \frac{y^{2}}{4} = 1

Choose the correct answer
The area of the circle $x^{2} + y^{2} = 16$ exterior to the parabola $y^{2} = 6 x$ is
(a) $\frac{4}{3} (4 π - \sqrt{3})$ (b) $\frac{4}{3} (4 π + \sqrt{3})$
(c) $\frac{4}{3} (8 π - \sqrt{3})$ (d) $\frac{4}{3} (8 π + \sqrt{3})$

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Graph x2+y2=4 in 3D looks like

Graph $x^{2} + y^{2} = 4$ in 3D looks like