Changing Dimensions of 3-D Figures Assignment and Quiz
A square pyramid has a base side length of 20.4 cm and a height of 18.2 cm. Which square pyramid is similar?
base side length = 30.6 cm, height = 27.3 cm
The rectangular prisms shown are similar. What is the area of the base of the smaller prism, rectangle ABCD?
1.26 cm2
The two hexagonal pyramids are similar. If the smaller pyramid has a surface area of 25.49 ft2, what is the surface area of the larger pyramid? Round to the nearest hundredth.
159.31 ft^2
The two triangular prisms shown are similar. The dimensions of the larger prism were multiplied by a scale factor of 4/5 to create the smaller prism. When the large prism was reduced, the surface area changed by a factor of
16/25
Two triangular pyramids are similar. The volume of the larger pyramid is 729 cm3 , and the volume of the smaller pyramid is 64 cm3. If the perimeter of the base of the smaller pyramid is 8 cm, what is the perimeter of the base of the larger pyramid?
18 cm
A shipping box in the shape of a cube has edge lengths of 6 inches. It can hold 24 staplers. If the dimensions of a shipping box are all doubled, how many staplers can the larger box hold?
192 staplers
The volumes of two similar solids are 729 inches3 and 125 inches3. If the surface area of the smaller solid is 74.32 inches2, what is the surface area of the larger solid? Round to the nearest hundredth.
240.80 in.2
The volume of a triangular prism is increased by a factor of 8. By what factor is the surface area of the figure increased?
4
A particular spherical-shaped fruit has a spherical seed, and the rest of the fruit is edible. The radius of the fruit is 3 times the radius of the seed. It is known that the seed has a volume of 100 cubic centimeters. What is the volume of edible fruit rounded to the nearest cubic centimeter?
A particular spherical-shaped fruit has a spherical seed, and the rest of the fruit is edible. The radius of the fruit is 3 times the radius of the seed. It is known that the seed has a volume of 100 cubic centimeters. What is the volume of edible fruit rounded to the nearest cubic centimeter?
Which cone is similar to a right cone with a height of 3 ft and a base with a diameter of 5 ft?
D
A rectangular prism has a length of 4.2 cm, a width of 5.8 cm, and a height of 9.6 cm. A similar prism has a length of 14.7 cm, a width of 20.3 cm, and a height of 33.6 cm. The dimensions of the smaller prism are each multiplied by what factor to produce the corresponding dimensions of the larger prism?
3.5
Two similar pyramids have base areas of 12.2 cm2 and 16 cm2. The surface area of the larger pyramid is 56 cm2. What is the surface area of the smaller pyramid?
42.7
A box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side. If the length and width of the base are doubled, how many cubes could the new box hold?
48
Consider the right cones pictured below. Which value of x would make the two cones similar?
49/4
Two spheres have surface areas of 100π units2 and 36π units2. If the volume of the larger sphere is 500/3π units3, determine the following measures. scale factor = _________ radius of smaller sphere = _________ units radius of larger sphere = _________ units volume of smaller sphere = _________π units3
5/3 3 5 36
A shipping box in the shape of a cube has an edge length of 8 inches. It can hold 8 mugs with no extra space between them. If the dimensions of the shipping box are all doubled, what is the maximum number of mugs that the larger box can hold?
64
A cube has an edge length of 9 centimeters. If the side length is increased by a factor of 3, how much larger is the perimeter of a face of the new cube?
72 cm
A triangular prism has an equilateral base with each side of the triangle measuring 8.4 centimeters. The height of the prism is 10.2 centimeters. Which triangular prism is similar to the described prism?
D
The right rectangular prisms are similar. Which statements are correct? Check all that apply.
The angles in the smaller prism measure 90 degrees. The perimeter of the rectangular bases changes by a factor of 2. The area of the rectangular bases changes by a factor of 4.
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.
The bases are congruent. The volume of the first solid is twice as much as the volume of the second solid. If the dimensions of the second solid are x by x by h, the first solid has 4xh more surface area than the second solid.
