Question

A girl fills a cylindrical bucket 32 cm in height and 18 cm in radius with sand. She empties the bucket on ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, find the radius and slant height of the heap​

Answer 1

Answer:

ANSWER

Height of conical heap, h=24cm.

Let the radius of the conical heap be r cm.

Then, volume of conical heap

=

3/1 πr2h=(

3

1

×

7

22

×r

2

×24).

Volume of sand = Volume of cyledrical bucket = πr

2

h=(

7

22

×18×18×32)

Now, Volume of conical heap = Volume of sand

⇒(

3

1

×

7

22

×r

2

×24)=(

7

22

×18×18×32)

r=

(18×18×4)

=(18×2)cm=36cm

∴ Radius of the heap =36 cm

Answer 2

Answer:

• 36 cm
• 12√13 cm

Step-by-step explanation:

Given

• Height of cylinder = 32 cm
• Radius of cylinder = 18 cm
• A cylindrical bucket with sand is emptied and made a conical heap,
• Height of conical heap = 24 cm

To find

• Radius of the heap
• Slant height of the heap

Solution

Volume of sand = πr²h

• (22/7 × 18 × 18 × 32) cm³.

Height of conical heap,

• h = 24 cm

Let the radius be,

• r cm

Then, volume of cone is,

• 1/3 πr²h
• (1/3 × 22/7 × r² × 24) cm³.

ATP,

• Volume of conical heap = Volume of sand
• (1/3 × 22/7 × r² × 24) = (22/7 × 18 × 18 × 32)
• r² = (18 × 18 × 32 × 3)/24
• r² = (18 × 18 × 4)
• r² = 1296
• r = √1296
• r = 36

∴ Radius of the conical heap = 36 cm

Now, slant height (l),

• √h² + r²
• √(24)² + (36)²
• √1872
• 12√13

Hence, the slant height of the conical heap is 12√13 cm.