A semicircular sheet of metal of diameter 35cm is bent into an open conical cup find the depth and capacity of the cup
Answers
Answer:
Depth = 15.15 cm
Capacity = 1214.02 cm^3
Step-by-step explanation:
It is given that
A semicircular sheet of metal of diameter 35cm is bent into an open conical cup
To find the slant height of cone(l)
The slant height of cone is equal to the radius of semi circle
Diameter = 35
radius, r = 35/2 = 17.5
therefore, l = 17.5 cm
To find the radius of cone
The ratio of angle of semicircle to 360 is equal to ratio of radius of cone to slant height
Let r be the base radius of cone
180/360 = 1/2 = r/17.5
r = 17.5/2 = 8.75 cm
Radius r = 8.75 cm
To find the depth
Depth of cone equal to height of cone
Height h = square root (l^2 - r^2) = square root(17.5^2 - 8.75^2) = 15.15 cm
Depth = 15.15 cm
To find the capacity (volume) of cone
Volume = 1/3pr^2h
Volume V= 1/3 x 3.14 x (8.75)^2 x 15.15 = 1214.02 cm^3
Capacity = 1214.02 cm^3
Answer:
See The Attached part
