Can somebody explain how to solve the similar solids 15cm, 6cm and 5,x that is a cylinder and the triangle one 24mm and 8mm,4mm
To solve the similar solids, you need to find the ratio of corresponding sides of the two figures.
For the cylinder with dimensions 15cm, 6cm and 5cm, the corresponding sides are the heights of the cylinders.
Let x be the height of the smaller cylinder. Then, we have:
15/24 = 6/8 = 5/x
Simplifying this equation, we get:
x = 3.2 cm
So, the height of the smaller cylinder is 3.2 cm.
For the triangular prism with dimensions 24mm, 8mm, and 4mm, the corresponding sides are the heights of the prism.
Let y be the height of the smaller prism. Then, we have:
24/8 = y/4
Simplifying this equation, we get:
y = 12 mm
So, the height of the smaller prism is 12 mm.
Thank you so much but it's still a little hard to understand 😇😇
I apologize if my explanation was difficult to understand. Let me try to explain it again using simpler terms.
The ratio of corresponding sides of similar solids is the same. In other words, if we have two solid figures that have the same shape but different sizes, then the ratio of any pair of corresponding sides of the two figures will be the same.
To find the height of the smaller cylinder and the smaller triangular prism, we need to use the ratio of the heights of the larger cylinder and triangular prism to the corresponding heights of the smaller ones.
For example, the height of the larger cylinder is 15cm. The corresponding height of the smaller cylinder is x. We know that the ratio of the heights is the same, so we can write:
15/24 = x/8
This means that the height of the smaller cylinder is 8/24 times (or 1/3) the height of the larger cylinder. We can solve for x by cross-multiplying and simplifying:
15*8 = 24*x
x = 15*8/24
x = 5
Therefore, the height of the smaller cylinder is 5cm. You can use the same method to find the height of the smaller triangular prism by using the ratios of the heights:
24/8 = y/4
y = 24*4/8
y = 12
So, the height of the smaller triangular prism is 12mm.
Thank you so much 😊
You're welcome! Feel free to ask if you have any further questions or if there's anything else I can help you with.
To solve the problem, let's break it down into two parts: finding the missing dimensions of the cylinder and finding the missing dimensions of the triangle.
1. Finding the missing dimensions of the cylinder:
- The given dimensions of the similar solids are 15cm, 6cm, and 5cm. Let's label the missing dimension of the cylinder as "x".
- Since the solids are similar, the ratios of the corresponding dimensions will be equal. Therefore, we can set up the following proportion using the provided dimensions:
15 cm / 6 cm = 5 cm / x
Cross-multiplying gives us:
15 cm * x = 6 cm * 5 cm
Simplifying further:
15x = 30 cm²
Dividing both sides by 15:
x = 30 cm² / 15 cm
x = 2 cm
So, the missing dimension of the cylinder is 2 cm.
2. Finding the missing dimensions of the triangle:
- The given dimensions of the triangle are 24mm, 8mm, and 4mm. Again, let's label the missing dimension as "x".
- Since the solids are similar, the ratios of the corresponding dimensions will be equal. We can write the following proportion using the provided dimensions:
24 mm / 8 mm = x / 4 mm
Cross-multiplying gives us:
24 mm * 4 mm = 8 mm * x
Simplifying further:
96 mm² = 8x mm
Dividing both sides by 8:
x = 96 mm² / 8 mm
x = 12 mm
Therefore, the missing dimension of the triangle is 12 mm.
To summarize:
The missing dimension of the cylinder is 2 cm, and the missing dimension of the triangle is 12 mm.
To solve similar solids, we need to find a ratio between the corresponding sides of the two figures. In this case, we have a cylinder and a triangle.
For the cylinder, we are given the dimensions of 15cm, 6cm, and 5cm. Let's assign these values as follows: the height of the cylinder is 15cm, the radius of the base is 6cm, and the unknown side is represented by 'x'. Remember that the radius is half the diameter.
For the triangle, we are given the dimensions of 24mm, 8mm, and 4mm. Let's assign these values as follows: the height of the triangle is 24mm, the base is 8mm, and the unknown side is represented by 'x'.
To find the ratio between the corresponding sides, we take the corresponding dimensions and set up a proportion:
For the cylinder:
15cm / 6cm = 5cm / x
For the triangle:
24mm / 8mm = 4mm / x
Now, to solve for 'x', we can cross-multiply the proportions:
For the cylinder:
15cm * x = 6cm * 5cm
x = (6cm * 5cm) / 15cm = 2cm
For the triangle:
24mm * x = 8mm * 4mm
x = (8mm * 4mm) / 24mm = 1.33mm
So, the missing side 'x' for the cylinder is 2cm, and the missing side 'x' for the triangle is 1.33mm.