A Tractor Engine Has a Steel Component with a Circular $\mathbf { r } ( t ) = 6 \cos t \mathbf { i } + 6 \sin t \mathbf { j }$

question 86

Multiple Choice

A tractor engine has a steel component with a circular base modeled by the vector-valued function $\mathbf { r } ( t ) = 6 \cos t \mathbf { i } + 6 \sin t \mathbf { j }$ . Its height is given by $z = 1 + y ^ { 2 }$ . (All measurements of the component are given in centimeters.) Find the lateral surface area of the component. Round your answer to two decimal places.

• A) \(753.98 \mathrm {~cm} ^ { 2 }\)
• B) \(735.13 \mathrm {~cm} ^ { 2 }\)
• C) \(716.28 \mathrm {~cm} ^ { 2 }\)
• D) \(245.04 \mathrm {~cm} ^ { 2 }\)
• E) \(697.43 \mathrm {~cm} ^ { 2 }\)

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