A cone 7dm high and 6 dm in diameter is placed on the ground Sand is poured over it - Maths - Surface Areas and Volumes

Question

A cone 7dm high and 6 dm in diameter is placed on the ground
Sand is poured over it until conical heap 21 dm high and 33 dm
circumference at the bottom is formed Find how many m3
of sand is there?

Gursheen kaur. · Accepted Answer

Given: Diameter of cone placed on ground = 6 dm

Radius = 6/2 = 3 dm

Height = 7dm

Volume of cone which is placed on the ground= $\frac{1}{3} π r^{2} h = \frac{1}{3} \times \frac{22}{7} \times 3^{2} \times (7) = 66 {d m}^{3} = 0.066 m^{3}$

Now,

Height of cone when sand is poured = 21dm

Circumference = 2Πr

33=2Πr

r= 33/2Π

r=5.25dm

Volume of cone when sand is poured = $\frac{1}{3} π r^{2} h = \frac{1}{3} \times \frac{22}{7} \times {(5.25)}^{2} \times (21) = 606.375 {d m}^{3} = 0.606375 m^{3}$

Sand left = Volume of cone when sand is poured - Vol. of cone which is placed on ground

=0.606375-0.066

=0.540375 $m^{3}$

6

A cone 7dm high and 6 dm in diameter is placed on the ground. Sand is poured over it until conical heap 21 dm high and 33 dm circumference at the bottom is formed. Find how many m3 of sand is there?

A cone 7dm high and 6 dm in diameter is placed on the ground. Sand is poured over it until conical heap 21 dm high and 33 dm circumference at the bottom is formed. Find how many m³ of sand is there?