WORD PROBLEMS ON SIMILAR SOLIDS WORKSHEET

Problem 1 :

Triangles ABC and PQR are similar and the area of triangle ABC is 1.5 m². What is the area of triangle PQR?

Solution

Problem 2 :

Two spheres have surface areas of 201 cm² and 452 cm² respectively. Find the radius of the larger sphere.

Solution

Problem 3 :

The sides of a triangular stained glass window pane are 5 m, 6 m and 7 m. Another pane is similar to it with longest side 21 m. Find :

a) The scale factor b the lengths of the other two sides

c) The ratio of the areas of the two panes.

Solution

Problem 4 :

Two rectangular photographs are similar and one has area double the other.

a) What is the scale factor?

b) If the larger one is 20 cm by 10 cm, what are the dimensions of the smaller one?

Solution

Problem 5 :

Two circles are such that one has area three times the other.

a) What is the scale factor?

b) If the smaller circle has a circumference of 35.8 m, what is the circumference of the larger one?

Solution

Problem 6 :

Here are two supermarket price tickets

The two supermarket price tickets are mathematically similar. The area of the smaller ticket is 7 cm². Calculate the area of the larger ticket.

Solution

Problem 7 :

Quadrilateral P is mathematically similar to quadrilateral Q

a) Calculate the value of x

b) Calculate the value of y

The area of quadrilateral P is 60 cm²

c) Calculate the area of quadrilateral Q

Solution

Problem 1 :

Two soup cans are similar and have heights of 8 cm and 16 cm respectively. Cylinder A has volume 225 cm³.

Find : a) the ratio of their radii.

b) the volume of B.

Solution

The following contain similar solids. Find the unknown length or volume :

Problem 2 :

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Problem 8 :

The ratio of the corresponding linear measures of two similar solids is 3:5. The volume of the smaller solid is 108 cubic inches. Describe and correct the error in fi nding the volume of the larger solid.

Solution

Problem 9 :

The ratio of the corresponding linear measures of two similar cans of fruit is 4 to 7. The smaller can has a surface area of 220 square centimeters. Find the surface area of the larger can.

Solution

Problem 10 :

The volume of a car engine is 390 cubic inches. Which scale model of the car has the greater engine volume, a 1:18 scale model or a 1:24 scale model? How much greater is it?

Solution

Problem 11 :

You have a small marble statue of Wolfgang Mozart. It is 10 inches tall and weighs 16 pounds. The original statue is 7 feet tall.

a) Estimate the weight of the original statue. Explain your reasoning.

b) If the original statue were 20 feet tall, how much would it weigh?

Solution

Consider the following similar shapes. Find

i) the scale factor

ii) the length or area marked by the unknown. 

Problem 1 :

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Problem 2 :

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Problem 7 :

Two similar triangles have a pair of corresponding sides of length 12 meters and 8 meters. The larger triangle has a perimeter of 48 meters and an area of 180 square meters. Find the perimeter and area of the smaller triangle.

Solution

Problem 8 :

You are making a scale model of a rectangular park for a school project. Your model has a length of 2 feet and a width of 1.4 feet. The actual park is 800 yards long. What are the perimeter and area of the actual park?

Solution

Problem 9 :

Figure A has an area of 48 square feet and one of the side lengths is 6 feet. Figure B has an area of 75 square feet. When the figures are similar, find the missing corresponding side length.

Solution

Problem 10 :

Figure A has an area of 18 square feet. Figure B has an area of 98 square feet and one of the side lengths is 14 feet. When the figures are similar, find the missing corresponding side length.

Solution

Problem 11 :

In the following exercises, JKLM ∼ EFGH.

a)  Find the scale factor of JKLM to EFGH.

b) Find the scale factor of EFGH to JKLM.

c) Find the values of x, y, and z.

Solution