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Diameter of a sphere is 21 dm. Find its surface area.
A. 1386 \[d{{m}^{2}}\]
B. 1376 \[d{{m}^{2}}\]
C. 1356 \[d{{m}^{2}}\]
D. 1380 \[d{{m}^{2}}\]

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Last updated date: 05th Mar 2024
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IVSAT 2024
Answer
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Hint: In this problem, we have to find the surface area with the given diameter. We know that the diameter is equal to half radius. We also know the formula for the surface area of the sphere, to find the surface area, we need to find the radius form the given diameter. We can substitute the radius in the surface area formula and the value if pi, to get the required answer.

Complete step by step answer:
We know that the formula of surface area of sphere is,
\[4\pi {{r}^{2}}\] …… (1)
We also know that the given diameter is 21 dm.
We can now find the radius of the sphere.
We know that the radius is half of the diameter.
Radius = \[\dfrac{diameter}{2}\].
We can substitute the given value of diameter, we get
Radius = \[\dfrac{21}{2}\]
Radius = 10.5dm.
We also know that \[\pi =\dfrac{22}{7}\], we can now substitute the pi value and the radius value in the formula (1), we get
Surface area of sphere = \[4\times \left( \dfrac{22}{7} \right)\times {{\left( 10.5 \right)}^{2}}=1386d{{m}^{2}}\].

So, the correct answer is “Option A”.

Note: Students make mistakes, while finding the value for pi, which should be remembered. We should also know some formula for shapes, to solve these types of problems. We also know the formula for the surface area of the sphere.
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