Question

The internal and external diameter of a hollow hemispherical vessel are 21 cm and 28 cm respectively. Find :

1. internal curved surface area,
2. external curved surface area,
3. total surface area,
4. volume of material of the vessel.

Answer 1

External radius (R) = 14 cm 

Internal radius (r) = `21/2 cm` 

i. Internal curved surface area

= 2πr² 

= `2 xx 22/7 xx 21/2 xx 21/2` 

= 693 cm² 

ii. External curved surface area

= 2πR² 

= `2 xx 22/7 xx 14 xx 14` 

= 1232 cm²

iii. Total surface area

= 2πR² + 2πr² + π(R² – r²) 

= `693 + 1232 + 22/7((14)^2 - (21/2)^2)` 

= `1925 + 22/7(196 - 441/4)` 

= `1925 + 22/7 xx 343/4`

= 1925 + 269.5

= 2194.5 cm³ 

iv. Volume of material used

= `2/3pi(R^3 - r^3)` 

= `2/3 xx 22/7((14)^3 - (21/2)^3)` 

= `44/21(2744 - 1157.625)` 

= `44/21 xx 1586.375`  

= 3323.83 cm³