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Question
The internal and external diameter of a hollow hemispherical vessel are 21 cm and 28 cm respectively. Find :
- internal curved surface area,
- external curved surface area,
- total surface area,
- volume of material of the vessel.
Solution
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
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