A cylindrical bucket, 32 cm high and with radius of base 18 cm , is filled with sand . This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap
Answers
Answer:
Radius = 5.14 or 36/7 , Slant Height = 24.54 cm
Step-by-step explanation:
To find the amount of sand we need to find the volume of sand.
Volume of a cylinder = π * r * r * height (radius = 18, height = 32)
22/7 * 18 * 18 * 32 = (22 * 324 * 32)/7 {Actual answer = 32572.03}
(For now we are keeping this value so it can be easy to cancel.)
As given in the question, the volume of cone = volume of cylinder.
(because the amount of sand on both the shapes are the same)
With this we can form an equation:
(22 * 324 * 32)/7 = 1/3 * π * r * r * height
22/7 * 324/7 *32/7 = 1/3 * 22/7 * r * r * height (perpendicular height)
324/7 *32/7 = 1/3 *r *r * 24 ( given in question)
324/7 = 7*32 * 1/3 * r* r * 24
324/7 = 7/4 *r * r
(324 * 4) / (7 * 7) = r * r
(18 * 2) / 7 = r
36/7 = r.
Using the Pythagorean Theorem:
Slant height (squared) = Radius (squared) + Perpendicular Height (squared)
= 36/7 (squared) + 24 (squared)
= 602.44898
Slant height = 602.44898 square root
= 24.54 cm
Pls mark me brainleiest.. :C
I did a lotta hard work for this.