a circular lamina is divided into two parts which can be bent so as to form the surfaces of two right circulars cones. I the areas of the conical surfaces are 2:1. Find the ratio of the volumes of the cones?
Answers
Answer:
Step-by-step explanation:
length of arc = 1/3 2π R. Circumference of base of circle = 2 π r
length of arc = 2/3 R x 2π r1
= r1 = 2/3 R
Slant height of cone = h1 = √l^2 - r1^2
= √l^2 - r1^2
slant height of cone = R
So h1 = √R^2 - (2/3 R)^2
= √5/9 R^2
= √5 / 3 R
We know volume of a cone = 1/3 π r1^2 h
V2 = 1/3 π (2/3 R)^2 x √5/3 R
Now circumference of base of circle = length of arc
2 π R = 1/3 2 π r
r = 1/3 R
slant height of cone is R
h = √l^2 - r^2
h = √R^2 - (R/3)^2
h = √8R^2/9
h = 2√2/3 R
Volume of a cone = V1 = 1/3 π r^2 h
V1 = 1/3 π (R/3)^2 2√2/3 R
The ratio is 2:1 .So
V2/V1 = 1/3 π (2/3 R)^2 x √5/3 R / 1/3 π (R/3)^2 2√2/3
V2/V1 = 2 √5 / √2
Hope it helps. Pls ignore the scratches of pen and the poor picture quality.
