Which of the following is the volume of the solid obtained if the triangle is revolved about its hypotenuse?
A)  3700/17 cub.unit
B)  4800/17 cub.unit
C)  3200/17 cub.unit
D)  3600/17 cub.unit
answer this question
Answers
Answer:
Object A: 3700/17 cub.unit is your answer
WHEN TRIANGLE IS REVOLVED ABOUT IT'S HYPOTENUSE THEN Double sided triangle are formed.
Given : A double cone is formed by revolving a right angled triangle having sides 8cm, 15cm and 17cm about its hypotenuse
To Find : volume of the solid obtained
Solution:
Right angle triangle is revolved about the hypotenuse AC, the figure so formed is a double cone.
Attached is figure
In triangle ABC,
AB = 8 cm
AC = 15 cm
BC = 17 cm
OB = h₁
OC = h₂
OA = OD = r
Area of ΔABC
(1/2) * AB * AC = (1/2) * BC * r
r = radius of base of cones formed
8 * 15 = 17 * r
=> r = 120/17
Volume = (1/3)πr² (h₁ + h₂)
= (1/3)πr² (17)
= (1/3)(120/17)² * 17
= 4800/17 cubic unit
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