SURFACE AREAS AND VOLUMES OF SIMILAR SOLIDS WORKSHEET

The scale factor between two similar figures is given. The surface area and volume of the smaller figure are given. Find the surface area and volume of the larger figure.

Problem 1 :

Scale factor = 1 : 2

SA = 90 yd²

V = 216 yd³

Solution

Problem 2 :

Scale factor = 4 : 9

SA = 256 km²

V = 1536 km³

Solution

Problem 3 :

The dimensions of the touch tank at an aquarium are doubled. What is the volume of the new touch tank?

A) 150 ft³       B) 4000 ft³    C) 8000 ft³    D) 16,000 ft³ 

Solution

The solids are similar. Find the volume of the red solid. Round your answer to the nearest tenth.

Problem 4 :

Solution

Problem 5 :

Solution

Each pair of figures is similar. Use the information given to find the scale factor of the figure on the left to the figure on the right. 

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

The solids are similar. Find the surface area S of the shaded shape.

Solution

Problem 4 :

The pyramids are similar. What is the surface area of Pyramid A?

Solution

Problem 5 :

Find the surface area of smaller cuboid.

Solution

Problem 6 :

Find the surface area of large cylinder.

Solution

Problem 7 :

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 8 :

A and B are mathematically similar.

The height of A : the height of B = 3 : 5

(a) Find the surface area of A : the surface area of B

(b) Find the volume of A : the volume of B

Solution

Problem 9 :

A, B and C are similar.

• The volume of A is 729 cm³ and the volume of B is 64 cm³.
• The surface area of B is 25 cm² and the surface area of C is 121 cm².
• Find the ratio length of A : length of B : length of C

Solution

Problem 10 :

Shapes A, B and C are similar.

• The height of shape A is 8 cm.
• The height of shape C is 4cm.
• The ratio of the surface area of shape B to the surface area of shape C is 25:9
• Work out the ratio of the volume of shape A to shape B.

Solution

The solids are similar. Find the surface area S of the red solid. Round your answer to the nearest tenth.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

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 4 :

A model of sky scraper was made with the scale factor of  3 : 13. What is the ratio of the surface area of model to the surface area of original sky scrapers?

Solution

Problem 5 :

Each pair of figures is similar. Find the scale factor of the figure on the left to the figure on the right. Then find

(i)  the ratio of surface areas

and

(ii)  the ratio of volumes.

Solution

Problem 6 :

Solution

Problem 7 :

Cylinders A and B are similar.

• The height of A is 6 cm.
• The volume of A is 240 cm³ to 2 significant figures.
• The height of B is 15 cm and the volume of B is y.

Work out the error interval of y. 

Solution

Problem 8 :

The square based pyramid A is divided into Pyramid B and Frustum C.

(a) Express the volume of Pyramid B as a fraction of the volume of Pyramid A.

(b) Express the volume of Frustum C as a fraction of the volume of Pyramid A.

Solution

Problem 9 :

Ornament A and B are mathematically similar. They are solid and both made from copper and zinc in the ratio 3:2

• Ornament A has a height of 5 cm and volume of 30 cm³
• Ornament B has a height of 18 cm. The density of copper is 8.96 g/cm³
• The density of zinc is 7.13 g/cm³

Work out the difference in mass between ornament A and ornament B.

Solution