Surface Area of a Sphere in Terms of Diameter

The surface area of a sphere in terms of diameter is the space occupied by the curved surface of the sphere in the terms of its diameter. A sphere is a three-dimensional round shape that does not have any edges or vertices. In this section, we will discuss the surface area of a sphere in terms of diameter along with solved examples. Let us start with the pre-required knowledge to understand the topic, surface area of a sphere in terms of diameter.

The surface area of a sphere in terms of diameter is the area covered by the curved surface of a sphere in the terms of its diameter. A sphere is a three-dimensional shape that is completely round in shape. Mathematically, a sphere is defined as the collection of points that are all at the same distance (r) from a common point (center of the sphere) in three-dimensional space. This common point is called the center of the sphere and the distance between any point and the center is called the radius of the sphere. The surface area of a sphere is given in terms of square units like m², cm², in² or ft², etc.

For a sphere, if its diameter is given, then its surface area can be given by πD².

Thus, the surface area of a Sphere (in terms of diameter) = Area of the curved surface of a sphere = πD²
The surface area of a Sphere (in terms of radius) = 4πr² where r is the radius of the sphere

• Step 1: Identify the diameter of the sphere and name it to be D.
• Step 2: Find the surface area of a sphere in terms of diameter using the formula πD².
• Step 3: Represent the final answer in square units.

Example: Find the surface area of a sphere having diameter = 7 units. (Use π = 22/7)

Solution: Given D = 7 units
Surface area of a hemisphere =  πD² =  (22/7)(7)² = 22 × 7 = 154 units²

Answer:  The surface area of the sphere =  154 units²

What is the Surface Area of a Sphere in Terms of Diameter?

The surface area of a sphere in terms of diameter is the amount of region covered by the sphere in the terms of its diameter. A sphere is a 3-D solid obtained which is a round shape that has no edges or vertices in it. The total surface area of a sphere is the same as its curved surface area due to the absence of edges or vertices.

What is the Formula of Surface Area of a Sphere in Terms of Diameter?

The formula of the surface area of a sphere in terms of diameter is given as, πD² where "D" is the diameter of the sphere. This formula shows the dependence of the surface area of a sphere on the diameter of the sphere.

What is the Unit of Surface Area of a Sphere in Terms of Diameter?

The unit of the surface area of a sphere in terms of diameter is given in square units, for example, m², cm², in² or ft², etc.

How to Find the Surface Area of a Sphere in Terms of Diameter?

• Step 1: Identify the diameter of the sphere.
• Step 2: Determine the surface area of a sphere in terms of diameter using the formula πD².
• Step 3: Now, represent the final answer in square units.

How to Find the Diameter of Sphere If the Surface Area of a Sphere in Terms of Diameter is Known?

• Step 1: Identify the given dimensions of the sphere and let it be "D".
• Step 2: Substitute the values in the formula πD².
• Step 3: Solve for "D" 
• Step 3: Now, represent the final answer in square units.

What Happens to the Surface Area of a Sphere in Terms of Diameter If Its Diameter is Doubled?

The surface area of a sphere in terms of diameter is quadrupled if its diameter is doubled as the "D" in the formula gets substituted as "2D" giving the formula πD² = π(2D)² = 4(πD²) which is four times the original surface area of the sphere.

What Happens to the Surface Area of a Sphere in Terms of Diameter If Its Diameter is Halved?

The surface area of a sphere in terms of diameter becomes one fourth its original value if its diameter is halved as the "D" in the formula gets substituted as "D/2" giving the formula πD² = π(D/2)² = (1/4) × (πD²) which is one fourth the original surface area of the sphere.