Question

Describe in words the region of double-struck R3 represented by the equation: x2 + z2 ≤ 36.

Answer 1

Explanation:

Given that:

`x^2 + z^2 \leq 36`

if we assume that x is zero, then
`z^2 = 36` ,
`z = \pm √(36)`
`z = \pm 6` i.e the radius of the circle goes from -6 to +6, Similarly, if we assume that z is zero, then
`x^2 = \pm 36` ,
`x = \pm √(36)` ,
`x = \pm 6` . This implies that
`x^2 + z^2` describes the circle with radius 6

`x^2 + z^2 \leq 36` is an equation at region which consist of those points whose distance from the centre is at least with radius -6 and at most 6.

Therefore, the region is the solid cylinder of radius 6, where the Y axis is also the axis of the cylinder.