Trivia Questions On Linear, Area And Volume Scale Factor! Quiz

Explanation
When the length and width of a rectangle are doubled, the area of the rectangle increases by a factor of 4. In this case, the original rectangle has an area of 5 cm2. When the length and width are doubled, the area of the enlarged rectangle becomes 5 cm2 * 4 = 20 cm2.

Explanation
If the lengths of the second shape are three times the corresponding lengths of the first shape, then the area of the second shape would be nine times the area of the first shape. Since the area of the first shape is 15cm2, the area of the second shape would be 15 x 9 = 135cm2.

Explanation
If the lengths of the second toy brick are twice the corresponding lengths of the first brick, then the surface area of the second brick would be four times the surface area of the first brick. Therefore, the surface area of the second brick would be 14 cm2 x 4 = 56 cm2.

If the lengths of the second toy brick are three times the corresponding lengths of the first brick, then the surface area of the second brick would be nine times the surface area of the first brick. Therefore, the surface area of the second brick would be 14 cm2 x 9 = 126 cm2.

Explanation
The volume of a similar brick with lengths twice the corresponding lengths of the first brick would be 2400 cm3. This is because the volume of a rectangular prism is calculated by multiplying the lengths of its three sides. If the lengths are doubled, the volume would be 2 times 2 times 2, which is equal to 8 times the original volume. Therefore, 300 cm3 multiplied by 8 is equal to 2400 cm3. Similarly, if the lengths are three times the corresponding lengths of the first brick, the volume would be 8100 cm3.

Explanation
The volume of a cylinder is calculated by multiplying the area of the base by the height. Since the two cans are similar, they have the same shape and proportions. Therefore, if the height of the second can is double the height of the first can, the volume of the second can will also be double the volume of the first can. Since the first can holds half a liter of paint, the second can would hold double that amount, which is 1 liter.

Explanation
To find the amount of paint needed to fill a similar can of height 45 cm, we can use the concept of ratios. Since the cans are similar, the ratio of their heights is the same as the ratio of their volumes. The height of the second can is 4.5 times the height of the first can (45 cm / 10 cm = 4.5). Therefore, the volume of the second can will be 4.5 times the volume of the first can. Since it takes 1 liter of paint to fill the first can, the second can will require 4.5 liters of paint (1 liter x 4.5 = 4.5 liters).

Explanation
When the dimensions of the can are increased by 1.5 times, the height of the can will become 12 cm * 1.5 = 18 cm. Since the can is similar, the ratio of the volumes of the two cans will be equal to the cube of the ratio of their corresponding dimensions. Therefore, the ratio of the volumes of the two cans will be (1.5)^3 = 3.375. Since it takes 2 liters of paint to fill the first can, it will take 2 liters * 3.375 = 6.75 liters of paint to fill the similar can.

Explanation
The volume of a statue is directly proportional to the cube of its height. Therefore, if the model statue is 10 cm high and has a volume of 100 cm3, we can use the proportionality to find the volume of the real statue.

Using the formula V = k * h^3, where V is the volume, k is the constant of proportionality, and h is the height, we can set up the equation:

100 = k * 10^3

Simplifying, we find that k = 100/1000 = 0.1

Now, we can substitute the height of the real statue (2.4 m) into the equation:

V = 0.1 * (2.4^3) = 1.38 m3

Therefore, the volume of the real statue is 1.38 m3.

Explanation
The area of a triangle is directly proportional to the square of its base. Therefore, if the area of the first triangle is 6 cm^2 with a base of 3 cm, and we want to find the base of a similar triangle with an area of 24 cm^2, we can set up a proportion. Since the areas are in a ratio of 1:4 (24/6 = 4), the bases will also be in a ratio of 1:2 (since the square root of 4 is 2). So, if the base of the first triangle is 3 cm, the base of the second triangle will be 3 cm multiplied by 2, which equals 6 cm.

Explanation
The capacity of the larger bottle can be found by using the ratio of their heights. Since the smaller bottle holds 850 ml, which is less than the capacity of the larger bottle, it can be assumed that the larger bottle is not completely filled. By setting up a proportion, we can find the capacity of the larger bottle. The ratio of the heights is 21 cm to 14 cm, which simplifies to 3:2. Therefore, the capacity of the larger bottle can be found by multiplying the capacity of the smaller bottle (850 ml) by the ratio of their heights (3/2), which equals 1275 ml or 1.275 liters. Rounded to 2 decimal places, the capacity of the larger bottle is 1.28 liters.