Table of Contents

- 1 How do you find the surface area and volume of a sphere?
- 2 How do you find the surface area when given the volume?
- 3 Can you convert volume to surface area?
- 4 What is the relationship between volume and surface area?
- 5 What is the formula for surface area of a prism?
- 6 What is the formula of surface area and volume?

## How do you find the surface area and volume of a sphere?

Sphere Formulas in terms of radius r:

- Volume of a sphere: V = (4/3)πr.
- Circumference of a sphere: C = 2πr.
- Surface area of a sphere: A = 4πr.

## How do you find the surface area when given the volume?

Surface Area Formulas:

- Volume = (1/3)πr2h.
- Lateral Surface Area = πrs = πr√(r2 + h2)
- Base Surface Area = πr2
- Total Surface Area. = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

**What is the surface area of this sphere?**

Therefore, the Surface Area of a Sphere with radius r equals 4πr2 .

**Why is the surface area of a sphere 4 pi r 2?**

One geometric explanation is that 4πr2 is the derivative of 43πr3, the volume of the ball with radius r, with respect to r. This is because if you enlarge r a little bit, the volume of the ball will change by its surface times the small enlargement of r.

### Can you convert volume to surface area?

For a cube, the equation for surface area is S=6*L*L, where L is the length of a side. Similarly, the volume of a cube is V =L*L*L. So for a cube, the ratio of surface area to volume is given by the ratio of these equations: S/V = 6/L.

### What is the relationship between volume and surface area?

Small or thin objects have a large surface area compared to the volume. This gives them a large ratio of surface to volume. Larger objects have small surface area compared to the volume so they have a small surface area to volume ratio.

**Does a sphere have a surface?**

A sphere has only a curved surface area. A sphere has no edges or vertices. All the surface points of the sphere are at an equal distance from the center.

**What is pi r2 4?**

The area of a circle is π multiplied by the square of the radius. The area of a circle when the radius ‘r’ is given is πr2. The area of a circle when the diameter ‘d’ is known is πd2/4. π is approx 3.14 or 22/7.

#### What is the formula for surface area of a prism?

The general formula for the total surface area of a right prism is T. S. A. =ph+2B where p represents the perimeter of the base, h the height of the prism and B the area of the base.

#### What is the formula of surface area and volume?

What is the formula of surface area and volume?

Shape | Total Surface Area | Volume formula |
---|---|---|

Cuboid | 2(lb+bh+hl) Where, l = length, b = breadth and h = height | Length x Width x Height |

Prism | ph+2B Where p= perimeter of the base, h = height and B =area of the base | Area of base x Height |