Pile of sand

A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.

Result

V =  3179.893 ft3

Solution:

$s = 20 \ ft \ \\ D = 31 \ ft \ \\ \ \\ r = D/2 = 31/2 = \dfrac{ 31 }{ 2 } = 15.5 \ ft \ \\ \ \\ S = \pi \cdot \ r^2 = 3.1416 \cdot \ 15.5^2 \doteq 754.7676 \ ft^2 \ \\ \ \\ s^2 = h^2 + r^2 \ \\ \ \\ h = \sqrt{ s^2-r^2 } = \sqrt{ 20^2-15.5^2 } \doteq 12.6392 \ ft \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ S \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 754.7676 \cdot \ 12.6392 \doteq 3179.8926 = 3179.893 \ ft^3$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Following knowledge from mathematics are needed to solve this word math problem:

Tip: Our volume units converter will help you with the conversion of volume units. Pythagorean theorem is the base for the right triangle calculator.

Next similar math problems:

1. Rectangular triangle PQR
In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal
2. Cone 15
The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height?
3. Slant height
The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
4. Holidays - on pool
Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
5. Truncated cone 5
The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone?
6. Chord
It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
7. A truck
A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
8. Chord circle
The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
9. Common chord
Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles?
10. Satin
Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?