The corresponding sides of two similar figures below are in the ratio 7:3:
State the length scale factor from the left figure to the right figure.
State the area scale factor from the left figure to the right figure.
Consider the two given triangles on the cartesian plane:
What scale factor is used to enlarge the small triangle?
What scale factor is used to reduce the large triangle?
Find the area of the small triangle
Find the area of the large triangle
Find the enlargement factor for the area of the small triangle
A triangle has side lengths of 7 cm, 10 cm and 16 cm. A similar triangle has an area that is 9 times the area of the first triangle.
Find the length scale factor between the two triangles.
Find the side lengths of the second triangle.
Describe the relationship between the perimeters of the two triangles.
Find the value of x in each of the following:
If a square with an area of 25\text{ m}^{2} is dilated by a factor of 0.4, find the side length of the dilated square.
The corresponding sides of two similar triangles are 8 \text{ cm} and 40 \text{ cm}.
Find the length scale factor between the two triangles.
If the area of the smaller triangle is 24\text{ cm}^{2}, find the area of the larger triangle.
A square of side length 6 cm is enlarged by a scale factor of 3. Find the area of the enlarged square.
The diameter of a circle is tripled. Describe what happens to its area.
The two pentagonal prisms are similar. The areas of their cross-sectional faces are given:
Find the surface area scale factor of Figure 2 compared to Figure 1.
Find the length scale factor.
Find the height of Figure 2, if Figure 1 is 13 mm high.
Consider the two similar rectangles shown below:
Find the area of rectangle A.
Find the area of rectangle B.
What is the ratio of the area of rectangle A to rectangle B?
Hence, if the matching sides of two similar figures are in the ratio m:n, what is the ratio of their corresponding areas?
Consider the formula A = \dfrac{1}{2} b h. If the values of both b and h are doubled, what effect does this have on A?
Consider the formula A = \pi r^{2}.
The cross-sectional areas of two similar rectangular prisms have dimensions: 6 cm by 9 cm, and 30 cm by 45 cm respectively.
Find the length scale factor.
Find the surface area scale factor.
Given that the surface area of the larger prism is 4425 \text{ cm}^{2}, find the surface area of the smaller prism.
Consider two similar parallelograms with matching sides in the ratio 6:8.
If the area of the smaller parallelogram is 72 \text{ cm}^{2}, calculate the area of the larger parallelogram.
Find the length of the base of the smaller parallelogram, if the length of the base of larger parallelogram is 12 cm.
Two similar parallelograms have sides in the ratio 2:3. If the area of the larger parallelogram is 45 \text{ cm}^{2}, find the area of the smaller parallelogram.
The volume of two similar crates are in the ratio 1331:125.
Find the ratio of their sides as an improper fraction.
Find the ratio of their surface areas as an improper fraction.
Consider the two similar trapezoidal prisms below:
Find the length scale factor from the smaller prism to the larger prism.
Find the volume scale factor from the smaller prism to the larger prism.
Consider the following two rectangular prisms:
Are the two rectangular prisms similar?
Find the length scale factor.
Find the surface area scale factor.
Find the volume scale factor.
Find the volume scale factor, if the measurements of the smaller prism are doubled.
Two similar cones have circular bases with radii 7 cm and 28 cm respectively.
Find the scale factor of the height of the smaller cone to the height of the larger cone.
Find the scale factor of the volume of the smaller cone to the volume of the larger cone.
Find the volume of the larger cone, if the volume of the smaller cone is 852 \text{ cm}^{3}.
The following two solids are similar. If the volume of the smaller solid is 193.7 \text{ cm}^{3} and the volume of the second is 24\,212.5 \text{ cm}^{3}, find the value of x.
The surface areas of two similar triangular prisms are in the ratio 64:49.
Find the ratio of their respective lengths.
Find the scale factor of their lengths.
Find the scale factor of their volumes.
Consider the two similar spheres shown. The smaller sphere has radius 3 cm while the larger sphere has a radius of 12 cm.
Find the volume of Sphere A, in exact form.
Find the volume of Sphere B, in exact form.
What is the ratio of the volume of Sphere A to Sphere B?
If the matching dimensions of two similar figures are in the ratio m:n, what ratio are their volumes in?
Two similar cylinders have volumes of 5760 \text{ cm}^{3}and 90 \text{ cm}^{3}:
Find the simplified ratio of the volume of the larger cylinder to the volume of the smaller cylinder.
Find the ratio of the height of the larger cylinder to the height of the smaller cylinder.
Hence, find the value of h.
The figure shows a rectangular field on which a game of tag is being played during a Physical Education class. To make it more of a fitness challenge, the teacher dilates the boundaries of the field by a factor of \\1.5. Find the area of the new field.
Consider two similar rectangular ceilings: the first with dimensions 5 m by 4 m, and the second with dimensions 20 m by 16 m.
Find the length enlargement factor.
Find the area enlargement factor.
The smaller ceiling took 1.5 L of paint to cover it. How many litres of paint would be required to paint the larger ceiling?
A rectangular billboard has a length of 1.2 m. The corresponding length on the designer's computer screen is 20 cm.
Find the length enlargement factor.
Find the area enlargement factor.
Find the area of the computer screen image of the billboard, if the area of the actual board is 86.4 \text{ m}^{2}.
Susana has two teddy bears that have the same shape but are different sizes. The length of the first teddy bear is 15 cm, while the length of the second teddy bear is 75 cm.
Find the length enlargement factor.
Find the surface area enlargement factor.
If the smaller bear needs 375 \text{ cm}^{2} of fake fur to be covered, find the area of fake fur needed to cover the bigger bear.
The dimensions of a cement slab are the length, l, the width, w, and the thickness, h. If these dimensions are tripled, what will happen to:
The surface are of the cement slab.
The volume of the cement slab.
The radii of two spherical balloons are 12 cm and 6 cm respectively.
Write down a simplified ratio for the radii.
Find the ratio of their surface areas.
Find the ratio of their volumes.
Find the ratio of their volumes, if half the air is released from the smaller balloon.
Valentina was making a trial birthday cake for her son. The dimensions are 10 cm for the length, 7 cm for the width and 3 cm for the height. The final cake needs to have dimensions of 20 cm for the length, 14 cm for the width and 6 cm for the height.
Find the ratio of the lengths of the final cake to those of the trial cake.
Hence, deduce the ratio of the volume of the final cake to that of the trial cake.
To make the final cake, what should Valentina multiply the quantities of the trial cake by?
A beehive consists of hexagonal prisms each with side length of 3.2 mm and depth of \\ 3.8 mm. A plastic container is built which is modelled on these hexagonal prisms, and has a side length of 6.4 cm.
Find the ratio of the side length of the hexagonal prisms in the beehive to the side length of the plastic container.
Find the ratio of the surface area of the side of the hexagonal prisms in the beehive to the surface area of the side of the plastic container.
Find the ratio of the volume of the hexagonal prisms in the beehive to the volume of the modelled plastic container.
A model of the Eiffel tower is made with a height ratio of 1:6480.
Find the height of the model, in cm, if the height of the Eiffel tower is 324 m.
Find the ratio of the surface area of the model to the surface area of the real Eiffel tower.
The ratio of the length of a model car to a real car is 1:20.
Find the ratio of the surface area of the model car to the surface area of the real car.
Find the ratio of the volume of the model car to the volume of the real car.
Find how many litres of paint are needed to paint the real car, if 18 mL are needed to paint the model car.
Find the capacity of the model car fuel tank, in mL, if the real car fuel tank holds 48 L.