4 points
A prism has a cross section
that is a regular twenty-sided
polygon.The volume of the
prism is 16,225 cm3 and its
length is 11 cm.Calculate the
side length of the cross-
section correct to 2 decimal
places.
O 6.79 cm
O
6.84 cm
O 17.07 cm
O
43.16 cm
Answers
Given : A prism has a cross section that is a regular twenty-sided
polygon. .The volume of the prism is 16,225 cm³
length is 11 cm
To Find : side length of the cross- section
Solution:
Side length = s cm
20 Sided polygon => n = 20
Area of n sided polygon = (1/4) ns²/tan(π/n)
= (1/4) 20s²/tan(π/20)
=> 5s²/tan9°
Hence cross section area = 5s²/tan9° cm²
Length = 11 cm
Volume = cross section area x length
=> 16,225 = (5s²/tan9° ) x 11
=> 1475 = 5s²/tan9°
=> 295 = s²/tan9°
=> s² = 295 x tan9°
=> s² = 295 x 0.1584
=> s² = 46.728
=> s = 6.8358 cm
=> s = 6.84 cm
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