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Question
The radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm and its height is 8 cm. Find its total surface area. [Use π = 3.14]
Solution
We have,
Height, h = 8 cm
Base radii, R = 18 cm and r = 12 cm
Also, the slant height, `l = sqrt(("R" - r)^2 + "h"^2)`
`=sqrt((18-12)^2+8^2)`
`= sqrt(6^2 + 8^2)`
`= sqrt(36+64)`
`= sqrt(100)`
= 10 cm
Now ,
Total surface area of the solid frustum `= pi ("R" + r)l + pi"R"^2 + pi"r"^2`
= 3.14 × (18 + 12) × 10 + 3.14 × 182 + 3.14 + 122
= 3.14 × 30 × 10 + 3.14 ×324×144
= 3.14 × (300 + 3324 + 144)
= 3.14 × 768
= 2411.52 cm2
So, the total surface area of the solid frustum is 2411.52 cm2.
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