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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 threedimensional 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 prerequired knowledge to understand the topic, surface area of a sphere in terms of diameter.
What is 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 threedimensional 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 threedimensional 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 m^{2}, cm^{2}, in^{2} or ft^{2}, etc.
Formula of Surface Area of a Sphere in Terms of Diameter
For a sphere, if its diameter is given, then its surface area can be given by πD^{2}.
Thus, the surface area of a Sphere (in terms of diameter) = Area of the curved surface of a sphere = πD^{2}
The surface area of a Sphere (in terms of radius) = 4πr^{2} where r is the radius of the sphere
How to Find the Surface Area of a Sphere in Terms of Diameter?
As we learned in the previous section, the surface area of a sphere is πD^{2}. Thus, we follow the steps shown below to find the surface area of a sphere in terms of diameter.
 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 πD^{2}.
 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 = πD^{2} = (22/7)(7)^{2} = 22 × 7 = 154 units^{2}
Answer: The surface area of the sphere = 154 units^{2}
Solved Examples on Surface Area of a Sphere in Terms of Diameter

Example 1: Find the surface area of a sphere with diameter = 21 units. (Use π = 22/7)
Solution: Given Diameter of the sphere (D) = 21 units
Surface area of a sphere = πD^{2} = (22/7) 21^{2} = 22 × 3 × 21 = 1386 units^{2}Answer: Surface area of the hemisphere = 1386 units^{2}

Example 2: Find the diameter of the hemisphere given its surface area is 308 units^{2}. (Use π = 22/7)
Solution: Given A = 308 units^{2}
⇒ π D^{2} = 308
⇒ D^{2} = 308/(2π) = 49
⇒ D = 7 unitsAnswer: Diameter of the sphere is 7 units
FAQs on the Surface Area of a Sphere in Terms of Diameter
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 3D 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, πD^{2} 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, m^{2}, cm^{2}, in^{2} or ft^{2}, etc.
How to Find the Surface Area of a Sphere in Terms of Diameter?
We use the steps shown below 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 πD^{2}.
 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?
We use the steps shown below to find the diameter of the sphere if the surface area of a sphere in terms of diameter.
 Step 1: Identify the given dimensions of the sphere and let it be "D".
 Step 2: Substitute the values in the formula πD^{2}.
 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 πD^{2} = π(2D)^{2} = 4(πD^{2}) 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 πD^{2} = π(D/2)^{2} = (1/4) × (πD^{2}) which is one fourth the original surface area of the sphere.
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