Question

Find the difference between total surface area and curved surface area of a hemisphere of radius 21 cm.
A. \[1376c{{m}^{2}}\]
B. \[1386c{{m}^{2}}\]
C. \[1396c{{m}^{2}}\]
D.\[1404c{{m}^{2}}\]

Answer 1

Hint: To solve the question, we have to apply the formula for calculating the total surface area and the curved surface area of the hemisphere for the given radius value of 21 cm. To solve further, we have to subtract the obtained values to calculate the difference between total surface area and curved surface area of the hemisphere of the given radius.

Complete step-by-step answer:
We know that the formula for curved surface area of hemisphere is given by \[2\pi {{r}^{2}}\]
where r is the radius of the hemisphere.
The given value for the radius of the hemisphere is equal to 21 cm.
By substituting the value of radius of the hemisphere in the above-mentioned formula, we get
The curved surface area of hemisphere
 \[\begin{align}
  & =2\pi {{(21)}^{2}} \\
 & =2\pi (441) \\
 & =\pi (882) \\
\end{align}\]
We know the value of \[\pi =\dfrac{22}{7}\]. Thus, we get
\[\begin{align}
  & =\dfrac{22}{7}\times 882 \\
 & =22\times 126 \\
 & =2772 \\
\end{align}\]
We know that the formula for total surface area of hemisphere is given by \[3\pi {{r}^{2}}\]
By substituting the value of radius of the hemisphere in the above-mentioned formula, we get
The total surface area of hemisphere
\[\begin{align}
  & =3\pi {{(21)}^{2}} \\
 & =3\pi (441) \\
 & =\pi (1323) \\
\end{align}\]
By substituting the value of \[\pi \], we get
\[\begin{align}
  & =\dfrac{22}{7}\times 1323 \\
 & =22\times 189 \\
 & =4158 \\
\end{align}\]
The difference between total surface area and curved surface area of hemisphere of the given radius
= total surface area of hemisphere - curved surface area of hemisphere
By substituting the above values, we get
= 4158 – 2772
= 1386
The difference between total surface area and curved surface area of hemisphere of the given radius is equal to \[1386c{{m}^{2}}\]
Hence, option (b) is the right choice.

Note: The possibility of mistake can be not applying the appropriate formula for calculating the total surface area and the curved surface area of the hemisphere of the given radius. The other possibility of mistake can be the calculation mistake since it involves large numbers calculation.