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.

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]

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.

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.

**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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