 9.10 Similarity in solid figures

Interactive practice questions

Consider the rectangular prisms A and B shown. a

Find the surface area of Rectangular Prism A.

b

Find the surface area of Rectangular Prism B.

c

What is the ratio of the surface area of Rectangular Prism A to Rectangular Prism B?

d

Is it true that if the matching sides of two similar figures are in the ratio $m$m:$3$3, then their surface areas are in the ratio $m^2$m2:$3^2$32?

True

A

False

B

True

A

False

B
Easy
Approx 6 minutes

Two similar cones have matching heights and radii whose lengths are in the ratio $7$7:$2$2. Find the ratio of their surface areas.

Two similar pyramids have matching sides in the ratio $2$2:$5$5. If the surface area of the larger pyramid is $250$250 cm2, find the surface area of the smaller pyramid.

Consider the two similar spheres shown. The smaller sphere has radius $3$3 cm while the larger sphere has a radius of $12$12 cm.

Outcomes

G.14a

Apply the concepts of similarity to two- or three-dimensional geometric figuresspecifically, compare ratios between lengths, perimeters, areas, and volumes of similar figures

G.14b

Apply the concepts of similarity to two- or three-dimensional geometric figuresspecifically, determine how changes in one or more dimensions of a figure affect area and/or volume of the figure

G.14c

Apply the concepts of similarity to two- or three-dimensional geometric figuresspecifically, determine how changes in area and/or volume of a figure affect one or more dimensions of the figure

G.14d

Apply the concepts of similarity to two- or three-dimensional geometric figuresspecifically, solve problems, including practical problems, about similar geometric figures