# Simplistic Surface Area Problem

#### apt403

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.

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: $$d$$

The cone has a slant height modeled by: $$d - .6$$

The cylinder's height is modeled by: $$d + 4$$

2. Relevant equations

As given by the book:

Surface area of cone:

$$\pi r(r + l)$$, where $$r$$ is the radius and $$l$$ is the slant height.

Surface area of cylinder:

$$2\pi r^2+2\pi rh$$, where $$r$$ is the radius and $$h$$ is the height.

3. The attempt at a solution

Cone surface area:

$$\pi (\frac {1}{2}d)((\frac {1}{2}d)+(d-.6))$$

Cylinder Surface Area:

$$2\pi ((\frac {1}{2}d))^2 + 2\pi (\frac {1}{2}d)(d + 4)$$

Combined formula:

$$\frac {299\pi}{4}$$

For the first problem, when $$d = 5$$, 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.

Last edited:

#### HallsofIvy

your formula for surface area of a cylinder includes the area of both ends. Since, here, you have the cone sitting on one end of the cylinder, you probably should not include that area.

#### apt403

your formula for surface area of a cylinder includes the area of both ends. Since, here, you have the cone sitting on one end of the cylinder, you probably should not include that area.
Yeah, that was my problem. Thanks a bunch.

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