A heap of water is in the form of a cone whose diameter is 10.5 m and hight is 3m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.
Answers
Answer:
Step-by-step explanation:
Diameter of a cone ( d ) = 10.5 m
Radius of a cone ( r ) = d / 2
r = 10.5 / 2 = 5.25 m
Volume of the heap ( volume of the cone )
V = ( π × r ^2 × h ) / 3
={ (22 / 7 ) × ( 5.25 )^2 × 3 } / 3
={ (3.14 ) × ( 5.25 ) × ( 5.25 ) × 3 } / 3
={ (3.14 ) × ( 27.56 ) × 3 } / 3
={ 86.54 × 3 } / 3
={ 259.62 } / 3
= 86.54 cubic. cm
Let the slant height of the cone = l cm
l^2 = r^2 + h^2
= 3^2 + ( 5.25 )^2
= 9 + 27.56
= 36.56
l = √36.56
l = 6.046 ( approx)
The area of the canvas required
= curved surface area of the cone
= π × r × l
= (3.14 ) × 5.25 × 6.046
= 16.485 × 6.046
= 99.67 cm^2
Answer:
Diameter = d = 10.5 m
Radius = r = d / 2
r = 10.5 / 2 = 5.25 m
i ) volume of the heap = volume of the cone
V = ( pi × r ^2 × h ) /3
= (22 / 7 ) × ( 5.25 )^2 × 3 / 3
= 86.625 cubic cm
ii ) let the slant height of the cone = l cm
l^2 = r^2 + h^2
= 3^2 + ( 5.25 )^2
= 9 + 27.5625
= 36.5625
Therefore ,
l = 6.046 ( approx)
The area of the canvas required to from rain
= curved surface area of the cone
= pi × r × l
= (22/ 7 ) × 5.25 × 6.046
= 697.62 / 7
= 99.66 cm^2