# 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:

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

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. See also our trigonometric triangle calculator.

## 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. 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.
5. 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
6. Cone
Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
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.
8. Thunderstorm
The height of the pole before the storm is 10 m. After a storm when they come to check it they see that on the ground from the pole blows part of the column. Distance from the pole is 3 meters. At how high was the pole broken? (In fact, a rectangular tria
9. Triangle P2
Can triangle have two right angles?
10. Calculate
Calculate the length of a side of the equilateral triangle with an area of 50cm2.
11. Center of the cube
Center of the cube has distance 33 cm from each vertex. Calculate the volume V and surface area S of the cube.