please answer this question plss help me . answer both question in detail plss
Answers
(a.) Step-by-step explanation:
In ∆ AOB, OD is the bisector of angle AOB
OA/OB =AD/DB---------------eq(1) [The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle]
In ∆BOC .OE is the bisector of angle BOC
OB/OC = BE/EC---------eq(2)
In ∆COA, OF is the bisector of angle COA
OC/OA =CF/FA-----------eq(3)
Multiplying eq 1, 2, 3
(OA/OB) * (OB/OC) * (OC/OA) = (AD/DB) * (BE/EC) * (CF/FA)
1= (AD/DB) * (BE/EC) * (CF/FA)
⇒DB*EC*FA = AD*BE*CF
#hence proved
(b.) Step-by-step explanation:
Let, the perpendicular height of cone be 'h'.
Let, the radius of base of cone be 'r'
Volume of cone =
\frac{1}{3} \pi {r}^{2} h
By given condition-
Volume of sphere = 2 × Volume of cone
\frac{2}{3} \pi {r}^{3} = 2 \times \frac{1}{3} \pi {r}^{2} h
After calculating,
r = h
Ans: The radius and height of cone must be equal to fill the spherical bowl in 2 attempts.
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