Questions and Answers

- 1.
### A rectangle has area 5cm

^{2}The length and width of this rectangle have been doubled. What is the area of the enlarged rectangle: ................cm^{2}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.Rate this question:

- 2.
### The shape has an area of 15cm

^{2}. What is the area of a similar shape whose lengths are three times the corresponding lengths of the first shape? ...............cm^{2}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.Rate this question:

- 3.
### A toy brick has a surface area of 14 cm

^{2}. What would be the surface area of a similar toy brick whose lengths are? a) twice the corresponding lengths of the first brick? ________ cm^{2}b) three times the corresponding lengths of the first brick? ________ cm^{2}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.Rate this question:

- 4.
### Brick has a volume of 300 cm3. What would be the volume of a similar brick whose lengths are a) twice the corresponding lengths of the first brick? ________ cm3 b) three times the corresponding lengths of the first brick? ________ cm3

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.Rate this question:

- 5.
### A can of paint, 6 cm high, holds half a liter of paint. How much paint would go into a similar can which is 12 cm high? .................litres

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.Rate this question:

- 6.
### It takes 1 liter of paint to fill a can of height 10 cm. How much paint does it take to fill a similar can of height 45 cm? .....................litres

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).Rate this question:

- 7.
### It takes 2 liters of paint to fill a can of height 12 cm. How much paint does it take to fill a similar can whose dimensions are 1.5 times the corresponding dimensions of the first can? ............................litres

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.Rate this question:

- 8.
### A model statue is 10 cm high and has a volume of 100 cm3. The real statue is 2.4 m high. What is the volume of the real statue? Give your answer, to 2 decimal places, in m3.

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.Rate this question:

- 9.
### A triangle has its base measuring 3 cm. Its area is 6 cm

^{2}. ow long are the base of a similar triangle that has an area of 24 cm^{2}?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.Rate this question:

- 10.
### Two similar bottles are 21 cm and 14 cm high. The smaller bottle holds 850 ml. Find the capacity of the larger one. Give your answers in litres, to 2 decimal places: ..............litres.

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.Rate this question:

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