Question

A bucket is in form of frustrum of a cone and holds 28.490 L
of water. The radii of the top and bottom are 14 cm and 21cm respectively. find the height of the bucket

Answer 1

volume of the frustrum =1/3 ×22/7×h(R^2+r^2+Rr)

28.490litres= 28490cu. cm.

volume of the bucket = 28490 cu. cm

1/3×22/7×h(21^2+14^2+21×14)=28490 cu.cm

1/3×22/7×h(931)=28490

20482/21×h=28490

h=598290/20482

h=29.2105263158cm

h=29.211 cm

Answer 2

Given:-

• Volume of frustum = 28.490l
• Top Radius (r1) = 14cm
• Bottom Radius (r2) = 21cm

To find:-

• Find the height of the bucket?

Solutions:-

• Let the height of the bucket be 'h' cm.

We know that;

• Volume of frustum => 1/3 πh[r1² + r2² + r1r2]

According to the questions;

=> 28.490 = 1/3 × 22/7 × h[(14)² + (21)² + 14 × 21]

=> 28.490 × 3 = 22/7 × h[196 + 441 + 294]

=> 85.47 = 22/7 × h × 931

=> 85.47 = 22 × h × 133

=> 85.47 = 2926 × h

=> 85.47/2926 = h

=> h = 0.029m

Hence, length of the frustum is 0.029m.

Some Important:-

Curved Surface Area and Total Surface Area of the Frustum

• The curved surface area of the frustum of the cone = π(R+r)l1

• The total surface area of the frustum of the cone = π l1 (R+r) +πR2 +πr2

• The slant height (l1) in both the cases shall be = √[H2 +(R-r)2]