Exam 20: Similarity

If a cube has edges that are 2 centimeters long, what is the total surface area of a larger similar cube with a scale factor of 2.3?

Consider the shape in the figure, made of centimeter cubes glued together face to face. A larger shape, similar to the one below, is also made of cubes. The larger shape is twice as tall, twice as wide, twice as deep, and in general twice as long in every corresponding length dimension. What is the volume of the larger shape, in cubic centimeters?

Complete the following sentences. A) A length of 3.8 centimeters is _____ times longer than 1.1 centimeters. B) A length of 24 inches is _____% as long as 36 inches. C) A change in the number of graduates from Smalltown High from 20 to 27 represents a _____% increase.

Refer to the similar figures below. What is the length of x, to the nearest tenth centimeter?

If the two polyhedra below are similar and oriented alike, then what are the values of x and y rounded to the nearest tenth?

Complete each statement. A) _____ is 25% of 200. B) _____ is 200% as much as 20. C) Thirty is 1 $\frac { 1 } { 2 }$ times more than _____.

Pinocchio's nose grew to four times its normal length. If the rest of Pinocchio's body grew in the same way, what would be his new surface area?

The two shapes below are similar. Find the missing angle size, y, and the missing length, x. Justify your answers.

Complete each statement. A) Kristin charges 25% less than what Beth charges for tutoring. Beth charges $30.00, so Kristin charges $_____. B) Twelve seconds is $\frac { 1 } { 3 }$ as much as _____ seconds. C) A 48° angle is 50% larger than a _____ degree angle.

Equilateral triangle X has sides 8 centimeters long, and equilateral triangle Y has sides 12 centimeters long. Are X and Y similar? Explain.

In map A, the distance from San Diego to Las Vegas is represented as 1.5 inches. The actual distance is 350 miles. In map B, the distance from San Diego to Las Vegas is represented as 2 inches, and the distance between Las Vegas and Ely, Nevada, is represented as 3 inches. What is the actual distance between Las Vegas and Ely? Write enough down to explain your thinking. (Hint: A diagram may help. Don't forget the units.)

A triangle is similar to a larger triangle that has lengths three times as long as the corresponding lengths in the smaller triangle. How large is the angle in the smaller triangle that corresponds to a 30° angle in the larger triangle?

Each face of the small cubes making the shape below has an area of 1 square unit. A) Surface area: _____ Volume: _____ B) Suppose another prism is similar to the one above but two times larger in all dimensions. What is the surface area and volume of the new prism? Write enough to make your thinking clear

Complete the following sentences. A) Eight feet is _____ times as long as six feet. B) Eight feet is _____ times longer than six feet.

Suppose triangle ABC is similar to triangle DEF with AB = 6, BC = 5, AC = 7, and DE = 10, all in centimeters. Assume $\angle A = \angle D , \angle B = \angle E , \angle C = \angle F$ A) Find the lengths of DF and EF. B) If the area of triangle ABC = about 15 cm², what is the area of triangle DEF? Justify your answer.

Every two right triangles are similar.

Are the two shaded triangles below similar? If so, then what is the scale factor? If not, why are they not similar?

A teacher has a model of an L-shaped building made of four cubes that snap together. She wants to make an enlargement, similar in shape to the original. She has only 600 cubes. What scale factor should she use to make the largest building possible? Explain your reasoning.

You want to make a larger, similar version of the trapezoid below so that the 4-centimeter side will be 10 centimeters in the larger version. A) How long will the other three sides of the larger trapezoid be? B) What are the sizes of the angles in the larger version?

Triangle A and triangle B are similar. The area of triangle A is 560 square centimeters. The area of triangle B is 35 square centimeters. How long would a segment in triangle A be if the corresponding segment in triangle B is 4 centimeters?