Simplistic Surface Area Problem

In summary, the conversation discusses finding the surface area of a cylinder with a right circular cone on top of it, both with equal base diameters. The surface area formulas for the cone and cylinder are given, but the correct answer is not matching the possible options. It is discovered that the formula for the cylinder includes the area of both ends, and since the cone is sitting on one end, that area should not be included in the calculation.
  • #1
apt403
47
0
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.

Homework Statement



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]

Homework 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.

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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  • #2
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.
 
  • #3
HallsofIvy said:
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.
 

Related to Simplistic Surface Area Problem

What is a "Simplistic Surface Area Problem"?

A Simplistic Surface Area Problem is a mathematical problem that involves finding the total area of a three-dimensional surface. It typically involves basic shapes such as cubes, rectangular prisms, or cylinders.

How is surface area calculated?

The formula for calculating surface area varies depending on the shape of the object. For example, the surface area of a cube is calculated by multiplying the length of one side by itself and then multiplying the result by six. The surface area of a cylinder is calculated by adding the areas of the circular bases and the curved surface area in between.

Why is surface area important?

Surface area is important in many fields, including architecture, engineering, and science. It allows us to determine the amount of material needed to cover or construct an object, as well as to calculate the amount of heat or energy that can be exchanged between an object and its surroundings.

What are some real-life examples of "Simplistic Surface Area Problems"?

Examples of Simplistic Surface Area Problems in real life include calculating the amount of paint needed to cover the walls of a room, determining the amount of wrapping paper needed to cover a gift box, and finding the surface area of a swimming pool to determine the amount of tiles needed to cover it.

How can I improve my skills in solving "Simplistic Surface Area Problems"?

The best way to improve your skills in solving Simplistic Surface Area Problems is to practice regularly with different types of shapes and scenarios. You can also seek out online resources, textbooks, or seek help from a math tutor to better understand the concepts and formulas involved.

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