GeoB_Wk14-12.9.1_Wayground Intro to Similar Solids Video Lesson

Mason is building two similar triangular pyramids for a school project. The surface area of the larger pyramid is 25 ft², and the surface area of the smaller pyramid is 4 ft². Find the following values for the pyramids, from left to right.

scale factor:​ (a)  

surface area ratio:​ (b)  

volume ratio:​ (c)  

Cone A ~ Cone B. The ratio of the surface area of Cone A to Cone B is 16:1.

Find the ratio of the radius of Cone A to Cone B, in fraction form.

David is packing gifts into two different rectangular boxes that are similar in shape. The smaller box has a volume of 15 cm³, and the larger box has a volume of 405 cm³. What is the ratio of the height of the smaller box to the height of the larger box?

If the prisms are similar, find the value of x.

____ cm

Maya and Scarlett each have a rectangular fish tank that are similar in shape. Maya's tank has a volume of 64 cm³ and Scarlett's tank has a volume of 216 cm³. What is the ratio of the heights of their tanks?

Priya is building two similar rectangular boxes for her art project. If the height of the larger box is 12 cm and the boxes are similar with a scale factor of 1:2, what is the height of the smaller box?

Emma is building two similar rectangular boxes for her art project. One box has a height of 5 cm and the other has a height of 15 cm. What is the ratio of the height of the smaller box to the larger box?

Aria and Samuel each have a cone-shaped water bottle. The bottles are similar in shape, and the scale factor between their sizes is 8/27. What is the ratio of the volumes of their water bottles?