# A concrete pedestal

A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.

Result

S3 =  33.836 ft2
S =  60.54 ft2
V =  32.07 ft3

#### Solution:

$h=2.5 \ \text{ft} \ \\ D_{1}=3 \ \text{ft} \ \\ D_{2}=5 \ \text{ft} \ \\ \ \\ \ \\ r=D_{1}/2=3/2=\dfrac{ 3 }{ 2 }=1.5 \ \text{ft} \ \\ R=D_{2}/2=5/2=\dfrac{ 5 }{ 2 }=2.5 \ \text{ft} \ \\ \ \\ l^2=h^2 + (R-r)^2 \ \\ l=\sqrt{ h^2 + (R-r)^2 }=\sqrt{ 2.5^2 + (2.5-1.5)^2 } \doteq 2.6926 \ \text{ft} \ \\ \ \\ S_{3}=\pi \cdot \ l \cdot \ (r+R)=3.1416 \cdot \ 2.6926 \cdot \ (1.5+2.5) \doteq 33.836 \doteq 33.836 \ \text{ft}^2$
$S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 1.5^2 \doteq 7.0686 \ \text{ft}^2 \ \\ S_{2}=\pi \cdot \ R^2=3.1416 \cdot \ 2.5^2 \doteq 19.635 \ \text{ft}^2 \ \\ \ \\ S=S_{1}+S_{2}+S_{3}=7.0686+19.635+33.836 \doteq 60.5395 \doteq 60.54 \ \text{ft}^2$
$V=\dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ h \cdot \ (r^2 + r \cdot \ R + R^2)=\dfrac{ 1 }{ 3 } \cdot \ 3.1416 \cdot \ 2.5 \cdot \ (1.5^2 + 1.5 \cdot \ 2.5 + 2.5^2) \doteq 32.0704 \doteq 32.07 \ \text{ft}^3$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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

Be the first to comment!

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

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

1. Tetrahedral pyramid
Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
2. Cone container
Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
3. Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
4. Roof of the church
The cone roof of the church has a diameter of 3m and a height of 4m. What is the size of the side edge of the church roof (s) and how much sheet will be needed to cover the church roof?
5. 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.
6. The diagram 2
The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
7. Slant height
The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
8. Cone
Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
9. Axial section of the cone
The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
11. Calculate
Calculate the length of a side of the equilateral triangle with an area of 50cm2.
12. The ditch
Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?
13. Median in right triangle
In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
14. Truncated cone
Calculate the volume of a truncated cone with base radiuses r1=13 cm, r2 = 10 cm and height v = 8 cm.
15. Volume of the cone
Find the volume of the cone with the base radius r and the height v. a) r = 6 cm, v = 8 cm b) r = 0,9 m, v = 2,3 m c) r = 1,4 dm, v = 30 dm
16. Axial cut
The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
17. Rotary cylinder 2
Base circumference of the rotary cylinder has same length as its height. What is the surface area of cylinder if its volume is 250 dm3?