Question

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​

Answer 1

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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