# A cylindrical bucket of height 32 cm and base radius 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

**Solution:**

Given, a cylindrical bucket is filled with sand.

Cylindrical bucket has a height 32 cm and a base radius of 18 cm.

Bucket is emptied on the ground and a conical heap of sand is formed.

Height of the conical heap of sand is 24 cm

We have to find the radius and slant height of the heap.

Volume of cylindrical bucket = πr²h

Given, r = 18 cm

h = 32 cm

Volume of sand in cylindrical bucket = (22/7)(18)²(32)

= 32585.14 cm³

Volume of cone = (1/3)πr²h

Given, h = 24 cm

= (1/3)(22/7)r²(24)

= 25.14r² cm³

Given, volume of sand in a cylindrical bucket = volume of conical heap of sand.

25.14r² = 32585.14

r² = 32585.14/25.14

r² = 1296.14

Taking square root,

r = √1296.14

r = 36 cm

Therefore, the radius of the conical heap of sand is 36 cm.

Slant height, l = √r² + h²

= √(36)² + (24)²

= √1296 + 576

= √1872

= 43.27 cm

Therefore, the slant height of the conical heap of sand is 43.27 cm.

**✦ Try This: **A cylindrical bucket of height 28 cm and base radius 14 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 20 cm, find the radius and slant height of the heap.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 13

**NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 13**

## A cylindrical bucket of height 32 cm and base radius 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

**Summary:**

A cylindrical bucket of height 32 cm and base radius 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, the radius and slant height of the heap is 36 cm and 43.27 cm

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