The area of the surface $\mathbf { r } ( u , v ) = 2 \cos u \mathbf { i } + 2 \sin u \mathbf { j } + v \mathbf { k }$ , where is

A)24?
B)18?
C)12?
D)6?
E)3?

Question

The area of the surface $\mathbf { r } ( u , v ) = 2 \cos u \mathbf { i } + 2 \sin u \mathbf { j } + v \mathbf { k }$ , where is

A)24?
B)18?
C)12?
D)6?
E)3?

Quizplus · Accepted Answer

The surface described is a cylinder with radius 2 and height 3 (since $v$ ranges from 0 to 3). The lateral surface area of a cylinder is given by $2\pi \times \text{radius} \times \text{height}$, which is $2\pi \times 2 \times 3 = 12$.

The Area of the Surface r(u,v)=2cos⁡ui+2sin⁡uj+vk\mathbf { r } ( u , v ) = 2 \cos u \mathbf { i } + 2 \sin u \mathbf { j } + v \mathbf { k }r(u,v)=2cosui+2sinuj+vk

The Area of the Surface $\mathbf { r } ( u , v ) = 2 \cos u \mathbf { i } + 2 \sin u \mathbf { j } + v \mathbf { k }$