Page 65 - Math Course 3 (Book 2)

Similar Solids

Real World Example
MO. 8 - L6b

Solve Problems Involving DOLLHOUSE
A small model of a fish tank for Eva's dollhouse is
Similar Solids built on a scale of 1 cm to 5 in. and has a volume of
24 cm³. What is the volume of the actual fish tank?

Let’s Begin

Find Surface Areas of Similar Solids

Example

A cylinder has a surface area of 245 square inches.
If the dimensions are doubled, what is the surface
area of the new cylinder?
1
a
Explore You know the scale factor is and
5
b
The cylinders are similar and the scale factor of the the volume of the model fish tank is 24
1
a
side lengths is .
b 2 cm³.
Therefore, surface areas of the rectangular prisms Plan Since the volumes have a ratio of ( )³
a
1
1
have a ratio of ( )² or ( )² a 1 b
2 2 and = , replace a with 1 and b with
5
b
a
Set up a proportion to find the surface area of the 5 in ( )³.
b
new cylinder.
a
Solve volume of model = ( )³ Write the ratio
volume of tank b
surface area of original cylinder = ( )² Write a Portion of volumes.
a
1
surface area of new cylinder b = ( )³ Replace a with
Substitute known 5 1 and b with 5.
1
245 = ( )² values. Let S = = 1 Simplify.
s 2 125
the surface area
of the new
cylinder. The volume of the actual tank is 125 times the
245 = 1 1 1 1 1 volume of the model.
s 4 ( )² = • or 4
2
2 2
The volume of the actual tank is
Find the cross
4 • 245 = S • 1 Answer 125 • 24 cm³ or 3000 cubic
products. centimeters.
980 = S Multiply.
Plan Use estimation to check the reasonable-
ness of this answer. 125 • 20 = 2500 and
The surface area of the new 125 • 30 = 3,750, so the answer must be
Answer
cylinder is 980 square inches. between 2,500 and 3,750. The answer is
3,000 cm³ is reasonable.

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