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

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