# Do similar cones have the same radius?

Table of Contents

## Do similar cones have the same radius?

Since the two cones are similar the ratios of the radius, height and slant height of the larger cone is some multiple of the radius, height and slant height of the smaller cone.

**How do you find the height of a similar cone?**

The slant height of a cone is given by the formula \[l = \sqrt {{r^2} + {h^2}} \], where \[r\] is the radius of the base of the cone, and \[h\] is the height of the cone.

### What does similar cones mean?

Similar cones and cylinders are those in which the axes and the diameters of the bases are proportional.

**How do you figure a ratio?**

To calculate the ratio of an amount we divide the amount by the total number of parts in the ratio and then multiply this answer by the original ratio. We want to work out $20 shared in the ratio of 1:3. Step 1 is to work out the total number of parts in the ratio. 1 + 3 = 4, so the ratio 1:3 contains 4 parts in total.

#### What makes cones similar?

**How do you find the ratio of surface area with similarity ratio?**

If two solids are similar, then the ratio of their surface areas is equal to the square of the ratio of their corresponding linear measures.

## What are similar cones?

**How do you find the volume of two similar figures?**

If two solids are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding sides. (Note that volume is not a “length” measurement – it is a 3-D measurement.)

### What is the volume of a similar cone?

The formula for the volume of a cone is V=1/3hπr². Learn how to use this formula to solve an example problem.

**How do you prove that a cone is similar?**

Let h1 and h2 be the lengths of the axes of two right circular cones. Let d1 and d2 be the lengths of the diameters of the bases of the two right circular cones. Then the two right circular cones are similar if and only if: h1h2=d1d2.