# Pyramid a+h

Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.

Result

S =  2376.169 cm2
V =  6760 cm3

#### Solution:

$a = 26 \ cm \ \\ v = 3 \cdot \ 10 = 30 \ cm \ \\ S_{ 1 } = a^2 = 26^2 = 676 \ cm^2 \ \\ h_{ 2 } = \sqrt{ v^2 + (a/2)^2 } = \sqrt{ 30^2 + (26/2)^2 } = \sqrt{ 1069 } \ cm \doteq 32.6956 \ cm \ \\ S_{ 2 } = a \cdot \ h_{ 2 }/2 = 26 \cdot \ 32.6956/2 = 13 \ \sqrt{ 1069 } \ cm^2 \doteq 425.0424 \ cm^2 \ \\ S = S_{ 1 }+4 \cdot \ S_{ 2 } = 676+4 \cdot \ 425.0424 \doteq 2376.1694 = 2376.169 \ cm^2$
$V = S_{ 1 } \cdot \ v/3 = 676 \cdot \ 30/3 = 6760 = 6760 \ cm^3$

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:

Do you want to convert length units? Do you know the volume and unit volume, and want to convert volume units? Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. 4side pyramid
Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
2. Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
3. Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
4. Axial section
Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
5. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
6. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
7. Cone
Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
8. Sphere slices
Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
9. Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
10. Cuboid
Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
11. Body diagonal
Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
12. 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.
13. Space diagonal
The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.