Right-angled trapezoid with the measure of the acute angle 50° is given. The lengths of its bases are 4 and 6 units. The volume of the solid obtained by rotation of the given trapezoid about the longer base is:
option
79.13cube units
83.29cube units
87.82 cube units
91.09 cube units
Given : Right-angled trapezoid with the measure of the acute angle 50° is given. The lengths of its bases are 4 and 6 units.
To Find : volume of the solid obtained by rotation of the given trapezoid about the longer base is:
79.13cube units
83.29 cube units
87.82 cube units
91.09 cube units
Solution:
Shape formed will be a cylinder surmounted with a cone
Cylinder height = 4 unit
Cone height = 6 – 4 = 2 unit
Cylinder / cone radius = 2 tan 50°
π ( 2 tan 50°)² 4 + (1/3) π ( 2 tan 50°)² 2
=( 8π / 3)tan² 50° ( 6 + 1)
= ( 8π / 3)tan² 50° ( 7)
π = 22/7
= ( 8* 22 /7 *3)tan² 50° ( 7)
= 176 tan² 50° / 3
= 83.3 cube units
Hence option 83.29 cube units is correct
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answer:
91.09
cube units