# Pyramid 8

Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.

Result

V =  641.27 cm3
S =  516.117 cm2

#### Solution:

$a=9 \ \text{cm} \ \\ S_{1}=a^2=9^2=81 \ \text{cm}^2 \ \\ s=a/2=9/2=\dfrac{ 9 }{ 2 }=4.5 \ \text{cm} \ \\ h=\sqrt{ 2 } \cdot \ s \cdot \ \tan ( 75 ^\circ \rightarrow\ \text{rad})=\sqrt{ 2 } \cdot \ s \cdot \ \tan ( 75 ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=\sqrt{ 2 } \cdot \ 4.5 \cdot \ \tan ( 75 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=23.75063 \ \\ h_{2}=\sqrt{ h^2 + s^2 }=\sqrt{ 23.7506^2 + 4.5^2 } \doteq 24.1732 \ \text{cm} \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{1} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 81 \cdot \ 23.7506 \doteq 641.2669 \doteq 641.27 \ \text{cm}^3$
$S_{2}=a \cdot \ h_{2} / 2=9 \cdot \ 24.1732 / 2 \doteq 108.7793 \ \text{cm}^2 \ \\ \ \\ S=S_{1} + 4 \cdot \ S_{2}=81 + 4 \cdot \ 108.7793 \doteq 516.1171 \doteq 516.117 \ \text{cm}^2$

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
Pythagorean theorem is the base for the right triangle calculator.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

## Next similar math problems:

1. Wall height
Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.
2. Pyramid
Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
3. Flowerbed
Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m2 =.
4. 4s pyramid
Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
5. Tetrahedron
What is the angle of the sides from the base of a three-sided pyramid where the sides are identical?
6. ABS CN
Calculate the absolute value of complex number -15-29i.
7. Perimeter of triangle
In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
8. Expression with powers
If x-1/x=5, find the value of x4+1/x4
9. Reference angle
Find the reference angle of each angle:
10. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
11. 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?
12. Maple
Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
13. If the
If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
14. Vector 7
Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
15. Coefficient
Determine the coefficient of this sequence: 7.2; 2.4; 0.8
16. KLM triangle
Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
17. Algebra
X+y=5, find xy (find the product of x and y if x+y = 5)