geometry

posted by .

Find the height of a cone with a volume of 138 cubic meters and a base area of 46 square meters

• geometry -

V = A * h

h = V / A = 138 / 46 = 3 m

• geometry -

Volume of a cone:

V = ( 1 / 3 ) * r ^ 2 * pi * h

r ^ 2 * pi = B

The area of the circle base

V = ( 1 / 3 ) * B * h

V = 138 m ^ 3

B = 46 m ^ 2

138 = ( 1 / 3 ) * 46 * h Multiply both sides by 3

3 * 138 = 1 * 46 * h

414 = 46 h Divide both sides by 46

414 / 46 = h

h = 414 / 46

-------------------------
Remark:

414 = 2 * 3 * 3 * 23

46 = 2 * 23

-------------------------

h = 2 * 3 * 3 * 23 / ( 2 * 23 )

h = 3 * 3

h = 9 m

Respond to this Question

 First Name School Subject Your Answer

Similar Questions

1. geometry

10. In cubic meters, how much greater is the volume of a cylinder with height 19 m and a radius 16 m than the volume of a square prism with height 19 m and base 16 m on a side?
2. math

1. find the lateral area of a right prism whose altitude measures 20 cm and whose base is a square with a width 7 cm long. 2. the volume of a rectangular solid is 5376 cubic meters, and the base is 24 meters by 16 meters. find the …
3. Math (Calculus)

A tank has the shape of an inverted circular cone with a base radius of 5 meters and a height of 20 meters. If water is being pumped into the tank at 2 cubic meters per minute, find the rate at which the water level is rising when …
4. geometry

A cone has a volume of 36pi cubic meters. Its height is four times its radius. Find the surface area of the cone.
5. geometry

Find the height of a cone with a volume of 138 cubic meters and a base area of 46 square meters
6. Geometry

For a given box, the height measures 4 meters. If the length of the rectangular base is 2 meters greater than the width of the base and the lateral area L is 96 square meters, find the dimensions of the box.
7. Geometry

find the radius of a sphere withh the given property. A.The number of square meters of a surface area equals the number of cubic meters of volume. B. The ratio of surface area in square meters to volume in cubic meters is 1:5.
8. 9th grade geometry

Rounded to the nearest hundred cubic meters, what is the total capacity (cone and cylinder) of the storage container?
9. Geometry

7. What is the surface area of a conical grain storage tank that has a height of 24 meters and a diameter of 16 meters?
10. Geometry

7. What is the surface area of a conical grain storage tank that has a height of 24 meters and a diameter of 16 meters?

More Similar Questions