If the area of triangle A is $$20\text{ cm}^2$$ and the area of triangle B is $$80\text{ cm}^2$$ , what is the ratio of their areas?

The ratio of the areas is $$\frac{80}{20} = 4$$ .

If the volume of a small bucket is $$500\text{ cm}^3$$ and the volume of a large bucket is $$13500\text{ cm}^3$$ , what is the ratio of their volumes?

The ratio of the volumes is $$\frac{13500}{500} = 27$$ .

If the surface area of shape A is $$80\text{ cm}^2$$ and the surface area of shape B is $$320\text{ cm}^2$$ , what is the ratio of their surface areas?

The ratio of the surface areas is $$\frac{320}{80} = 4$$ .

If the height of a small bucket is $$20\text{ cm}$$ and the height of a large bucket is $$40\text{ cm}$$ , what is the ratio of their heights?

The ratio of their heights is $$\frac{40}{20} = 2$$ .

What is the formula for the area of a triangle?

The area of a triangle is given by $$\frac{1}{2} \times \text{base} \times \text{height}$$ .

If the base of triangle A is $$4\text{ cm}$$ and the height is $$10\text{ cm}$$ , what is its area?

The area is $$\frac{1}{2} \times 4 \times 10 = 20\text{ cm}^2$$ .

What is the formula for the volume of a cylinder?

The volume of a cylinder is given by $$\text{Volume} = \text{base area} \times \text{height} = \text{π}r^2h$$ .

If the radius of a small can is $$2\text{ cm}$$ and the height is $$5\text{ cm}$$ , what is its volume?

The volume is $$\text{π} \times (2^2) \times 5 = 20\text{π} \text{ cm}^3$$ .

What is the significance of similar shapes in geometry?

Similar shapes have the same shape but different sizes, and their corresponding angles are equal while their corresponding sides are in proportion.

If two similar shapes have a side length ratio of 1:2, what is the ratio of their areas?

The ratio of their areas is $$1^2:2^2 = 1:4$$ .

If the volume of a small box is $$500\text{ cm}^3$$ , what is the volume of a similar box with a side length ratio of 3:1?

The volume of the larger box is $$500 \times 3^3 = 13500\text{ cm}^3$$ .

6.3 Practice - Area and Volume of Similar 3D Shapes Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the relationship between the areas of two similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

What is the formula for the volume of similar 3D shapes?

Back

The ratio of the volumes of two similar 3D shapes is equal to the cube of the ratio of their corresponding linear dimensions.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the relationship between the surface areas of two similar shapes?

Back

The ratio of the surface areas of two similar shapes is equal to the square of the ratio of their corresponding linear dimensions.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

How do you find the height of a larger similar shape if you know the height of a smaller one?

Back

Use the ratio of their volumes or areas to find the corresponding height.

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