Question

What is the volume of the figures pictured below?

Answer 1

The volume of figures is determined using different formulas that depend on the shapes involved, such as V = πr²h for cylinders and V = l × w × h for rectangular solids. Specific examples given include a cylinder of 9.278 cm³, a small box of 11.4 cm³, and a Rubik's cube of 185.2 cm³.

Step-by-step explanation:

To calculate the volume of the figures in the provided question, various formulas must be applied based on the shape of each figure. For example, to find the volume of a cylinder, we use the formula V = πr²h, where V represents the volume, r is the radius, and h is the height of the cylinder. As illustrated, the volume of a cylinder with a radius of 0.750 cm and a height of 5.25 cm is 9.278 cm³.

For rectangular boxes or cubes, the volume formula is V = l × w × h, where l, w, and h are the length, width, and height, respectively. According to the provided information, a small rectangular box with sides measuring 1.80 cm, 2.05 cm, and 3.1 cm has a volume of 11.4 cm³. Furthermore, a Rubik's cube with each side measuring 5.7 cm has a volume of 185.2 cm³ or 185.2 mL. Other volumes, such as those of the cubes mentioned in Figure 1.25 (a) and the blocks in the solution section, are calculated by multiplying the dimensions of length by width by height.

Answer 2

a. 5

b. 12

Step-by-step explanation:

Using the figures and the number of cubes used to build each one, we can see that the first figure (a) has a single row of three cubes with two additional cubes on each side, this is a total of 5 cubes, or a volume of 5 centimeter cubes. The second figure (b) has a face of two rows of three cubes or three columns of two cubes - either way 3 x 2 = 6 as well as an additional two rows of three cubes or three columns of two cubes behind those - 3 x 2 = 6. Adding the front and back: 6 + 6 = 12 centimeter cubes.