Question

A cylindrical bucket 32 CM high and with radius of base 18 cm ,is filled with sand. This bucket is empited on the ground and a conical heap of sand is formed. If the high of the conical heap is 24 cm, find the radius and slant height of the heap??​

Answer 1

Solution

Height of cylindrical bucket(h1)=32 cm

Radius of the base of the bucket (r1)=18 cm

∴Volume of the sand in the cylindrical bucket=πr12h1

Height of conical heap (h2)=24 cm

let the radius of the conical heap=r2

∴Volume of the sand in conical heap=31πr22h2

According to the question

The volume of the sand in the cylindrical bucket=Volume of the sand in the conical shape

πr12h1=31πr22h2

⇒π×(18)2×32=31π×r22×24

⇒r22=243×182×32

⇒r

Answer 2

Answer:

Height of cylindrical bucket(h

1

)=32 cm

Radius of the base of the bucket (r

1

)=18 cm

∴Volume of the sand in the cylindrical bucket=πr

1

2

h

1

Height of conical heap (h

2

)=24 cm

let the radius of the conical heap=r

2

∴Volume of the sand in conical heap=

3

1

πr

2

2

h

2

According to the question

The volume of the sand in the cylindrical bucket=Volume of the sand in the conical shape

πr

1

2

h

1

=

3

1

πr

2

2

h

2

⇒π×(18)

2

×32=

3

1

π×r

2

2

×24

⇒r

2

2

=

24

3×18

2

×32

⇒r

2

2

=18

2

×4

⇒r

2

=18×2=36cm

Slant height of heap=

r

2

2

+h

2

2

⇒

36

2

+24

2

⇒

1296+576

⇒

1872

⇒

144×13

⇒12

13

cm.