Question

What is the ratio for the surface areas of the cones shown below, given that they are similar and that the ratio of their radii and altitudes is 2:1? 25 7 35 A. 4:1 B. 1:8 C. 1:4 D. 8:1​

Answer 1

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

Z -----> the scale factor

In this problem

The scale factor is equal to

z = ² ----> the ratio of its corresponding radii or its corresponding altitudes

step 2

Find the ratio for the surface areas of the coneswe know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

Z -----> the scale factor

X ----> the surface area of the larger cone

y ----> the surface area of the smaller

cone

z² Y

we have

2 =

substitute

(²)² = ² Y

4

The ratio for the surface areas is equal to 4

That means-----> The surface area of the larger cone is 4 times the surface area of the smaller cone

Answer 2

Answer:

The ratio for the surface areas of the cones is 4:1.

Option A is the correct answer.

Step-by-step explanation:

Given

Two cones  one is smaller and the other is larger and both are similar

The ratio of radii and height of the cone is 2:1

To find the ratio for the surface areas of the cones

Solution:

Let the area of the large cone be 'x' and the smaller one be 'y'

We know,

The area of two similar figures is proportional to the squares of their corresponding sides and the ratio is called the scale factor.

Again

Let the scale factor be 'z'. So, the equation becomes:

$\frac{x}{y} =z^{2}.....eq. i$

According to question, z=2/1

Putting the value of z in eq. i

$\frac{x}{y} =\frac{2}{1} ^{2} \\\\or, \frac{x}{y} =4\\\\\\Converting into the ratio\\x:y=4:1$

Thus, the ratio for the surface areas of the cones is 4:1.

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