A bucket shaped like a frustum is 21 cm deep and its open top has radius 12 cm. It holds exactly 4.158 litres. Find the radius of its flat bottom. (Take \π = 22/7 , 1 litre = 1000 cm³.)

Question

Accepted Answer

3 cm. 4.158 litres = 4158 cm³. Since 1/3 × 22/7 × 21 = 22 , we get 22(144 + r² + 12r) = 4158, so 144 + r² + 12r = 189, i.e. r² + 12r - 45 = 0 = (r + 15)(r - 3). Hence r = 3 cm. 6.71 cm comes from dropping the Rr term and solving r² = 45; 13.75 cm treats the bucket as a cone of radius r; 7.94 cm treats it as a cylinder of radius r.

A bucket shaped like a frustum is 21 cm deep and its open top has radius 12 cm. It holds exactly 4.158 litres. Find the radius of its flat bottom. (Take $π = \frac{22}{7}$ , 1 litre = $1000 cm^{3} .$ )

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Frustum of a Cone practice

A bucket shaped like a frustum is 21 cm deep and its open top has radius 12 cm. It holds exactly 4.158 litres. Find the radius of its flat bottom. (Take π=722​, 1 litre = 1000cm3.)

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Frustum of a Cone practice

A bucket shaped like a frustum is 21 cm deep and its open top has radius 12 cm. It holds exactly 4.158 litres. Find the radius of its flat bottom. (Take $π = \frac{22}{7}$ , 1 litre = $1000 cm^{3} .$ )