I stumbled across a problem in one of my old math books, and the answer key is either wrong, or there's something I'm missing.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

All units are in inches.

Find the approx. surface area (in inches squared) of this object: A cylinder with a right circular cone on top of it, both with equal base diameters.

The diameter of the cone & cylinder base: [tex]d[/tex]

The cone has a slant height modeled by: [tex]d - .6[/tex]

The cylinder's height is modeled by: [tex]d + 4[/tex]

2. Relevant equations

As given by the book:

Surface area of cone:

[tex]\pi r(r + l)[/tex], where [tex]r[/tex] is the radius and [tex]l[/tex] is the slant height.

Surface area of cylinder:

[tex]2\pi r^2+2\pi rh[/tex], where [tex]r[/tex] is the radius and [tex]h[/tex] is the height.

3. The attempt at a solution

Cone surface area:

[tex]\pi (\frac {1}{2}d)((\frac {1}{2}d)+(d-.6))[/tex]

Cylinder Surface Area:

[tex]2\pi ((\frac {1}{2}d))^2 + 2\pi (\frac {1}{2}d)(d + 4)[/tex]

Combined formula:

[tex]\frac {299\pi}{4}[/tex]

For the first problem, when [tex]d = 5[/tex], my possible answers (in inches squared) are 278, 196, 44, and 38. But I keep getting 234.834! I know it asks for an approximate number, but 234 is way off from any of the answers.

Any insight to what I'm doing wrong?

Thanks.

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# Homework Help: Simplistic Surface Area Problem

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