The outer and inner radii of a hemisphere are 3 cm and 2 cm, then Tota

1.	The outer and inner radii of a hemisphere are 3 cm and 2 cm, then Total Surface Area (TSA) is ……… cm2A) 9.7B) 97 \(\frac37\)C) 96 \(\frac12\)D) 16 \(\frac14\)
Answer» Correct option is: B) \( 97 \frac 37 \, cm^2\) Inner radius of hemisphere is r = 2 cm and outer radius of hemisphere is R = 3 cm. \(\therefore\) Total surface area of hollow hemispherical cell = \(2 \pi r^2 + 2 \pi R^2 + \pi (R^2-r^2)\) = \(\pi (2 r^2 + 2 R^2 + R^2-r^2)\) = \(\pi (3 R^2 + r^2)\) = \(\frac {22}7\) ( \(3 \times 3^2 + 2^2\) ) = \(\frac {22}7\) (27 + 4) = \(\frac {22\times 31}7 = \frac {681}7 = 97 \frac 37 \, cm^2\) \(\therefore\) TSA of hollow hemispherical cell is \( 97 \frac 37 \, cm^2\) Correct option is: B) 97 \(\frac{3}{7}\)

The outer and inner radii of a hemisphere are 3 cm and 2 cm, then Total Surface Area (TSA) is ……… cm2A) 9.7B) 97 \(\frac37\)C) 96 \(\frac12\)D) 16 \(\frac14\)

Answer»

Correct option is: B) \( 97 \frac 37 \, cm^2\)

Inner radius of hemisphere is r = 2 cm and outer radius of hemisphere is R = 3 cm.

\(\therefore\) Total surface area of hollow hemispherical cell

= \(2 \pi r^2 + 2 \pi R^2 + \pi (R^2-r^2)\)

= \(\pi (2 r^2 + 2 R^2 + R^2-r^2)\)

= \(\pi (3 R^2 + r^2)\)

= \(\frac {22}7\) ( \(3 \times 3^2 + 2^2\) )

= \(\frac {22}7\) (27 + 4)

= \(\frac {22\times 31}7 = \frac {681}7 = 97 \frac 37 \, cm^2\)

\(\therefore\) TSA of hollow hemispherical cell is \( 97 \frac 37 \, cm^2\)

Correct option is: B) 97 \(\frac{3}{7}\)