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Before the ratio can be calculated, both lengths need to have the same units of measure. The length of the real basketball court is meters and the length of the scale model is centimeters. Convert meters to centimeters to have same units of measure. Next, calculate the ratio of the length of the model to the corresponding actual length in centimeters. The scale factor of the model will be $\tfrac{2}{175}$ or $2:175.$ Recall that the perimeter of a rectangle is two times the sum of its length and width. The perimeter of the real basketball court is meters. Since the miniature model of the court and the real court are similar rectangles, the ratio of their perimeters is equal to the ratio of their corresponding side lengths, or the scale factor. The scale factor is $\tfrac{2}{175}.$ Substitute the scale factor and the perimeter of the real basketball court into the equation and solve for The perimeter of the model is about meters. Finally, convert it to centimeters. The model basketball court has a perimeter of about centimeters.

The scale model of the stand and the real stand have to be similar figures, so they have the same ratio between their corresponding side lengths. This ratio is called the scale factor. Tadeo wants to create the model with a centimeter height. He knows that the height of the real stand is meters. Before finding the scale factor, both lengths must be in the same units. To achieve this, convert the height of the real stands from meters to centimeters. Now the ratio of the height of the model to the corresponding actual height can be calculated. The scale factor of the model will be $\tfrac{1}{25},$ or $1:25.$ This means that the dimensions of the model stand will be times smaller than the dimensions of the real stand. Since it is a right triangle, the Pythagorean theorem can be used to find The base length of the triangular figure is meters. Now, calculate the area of the triangle as half of the product of the base and height. The area of the triangular side of the real stand is square meters. Recall that if two figures are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths. The ratio of the corresponding side lengths is equal to the length scale factor, so in this case, $k=\tfrac{1}{25}.$ The square of this scale factor can be used to find the area of the model's triangular side. The area of the model's triangular side is $0.0096$ square meters. Finally, convert it to square centimeters. The area of the triangular side of Tadeo's model is square centimeters.

While a sphere does not have any sides, its radius can be considered as a side measurement for the scale factor. Tadeo first wants to find the surface area of the real ball. Remember the formula for the surface area of a sphere. Since the radius of the real basketball is given to be inches, substitute into the formula and simplify to find the surface area of the basketball. The surface area of the real basketball is Next, use the square of the given scale factor to find the surface area of the miniature ball. Since the scale factor is given as the ratio of the miniature ball to the real ball, should corresponds to the surface area of the miniature ball. The surface area of the miniature ball will be about  square inches. The radius of the real basketball is inches and the length scale factor is Substitute these values into the equation and solve it for The radius of the miniature ball will be about inches.

Since the miniature stadium is a scale model, the actual stadium and the miniature stadium are similar solids. Recall that the ratio of the volumes of similar solids is equal to the cube of the length scale factor Note that the scale factor is equal to the ratio of the corresponding side lengths. The length scale factor is and the volume of the real stadium is cubic meters. Then, the volume of the miniature stadium can be found by substituting and into the formula and solving for The volume of the miniature stadium will be about cubic meters.

Start by determining the length scale factor, the ratio of the given lengths. Both lengths need to have the same units of measure, so remember to convert meters to centimeters using the conversion factor Now the two centimeter lengths can be used to write the length scale factor Tadeo claims that the weights of the action figure and the human player are proportional to the cube of the scale factor because they are similar solids. Calculate the weight of the player using this information. The action figure of player weighs pounds, so substitute the weight of the action figure and the scale factor into the equation. According to these calculations, the human basketball player must weigh about pounds! 😱 Tadeo knows that even the heaviest NBA player of all time weighed about pounds. The calculated value does not make sense because the density of an action figure and the density of a person are different. This means that the weights of the action figure and the player are not directly related to the volume scale factor.