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The lower portion of a haystack is an inverted conc frustum and upper part is a cone as shown in figure. Find the total volume of the haystack where $A B = 3 cm$ and $CD = 2 cm$

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35.66 c m 2

135.66 c m 2

145.6 c m 2

15.66 c m 2

answer is B.

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Detailed Solution

Given is a figure,
Question Image

Volume of a frustum

= 13 π R 2 + r 2 + R r × h

Here, R is bigger radius, r is smaller radius, h is height.
Volume of a cone

= 13 π r 2 h

Here, r is radius, h is height.
Now,
Volume of the haystack = volume of cone + volume of the frustum

⇒ 13 π R 2 + r 2 + R r × h 1 + 13 π R 2 h 2 ⇒ 13 π 32 + 22 + 6 × 3.5 + 13 π × 32 × 7 ⇒ 22 3 × 7 × 19 × 3.5 + 9 × 7 ⇒ 135.66 c m 2

Thus, the total volume of the haystack is

135.66 c m 2

.
Therefore, option (2) is correct.

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