http://www.ck12.org Chapter 11. Surface Area and Volume
- Find the volume of the pyramid.
- A rectangular pyramid has a base area of 56cm^2 and a volume of 224cm^3. What is the height of the pyramid?
Answers:
- The area of the base isA=^14 s^2
√
3 because it is an equilateral triangle.B=
1
4
82
√
3 = 16
√
3
SA= 16
√
3 +
1
2
( 24 )( 18 ) = 16
√
3 + 216 ≈ 243. 71
- In the formula for surface area, the lateral surface area is^12 Plor^12 nbl. We know thatn=4 andb=l. Let’s solve
forb.
1
2
nbl= 72 f t^2
1
2( 4 )b^2 = 72
2 b^2 = 72
b^2 = 36
b= 6Therefore, the base edges are all 6 units and the slant height is also 6 units.
- To find the area of the base, we need to find the apothem. If the base edges are 10 units, then the apothem is 5
√
3
for a regular hexagon. The area of the base is^12 asn=^12
(
5
√
3
)
( 10 )( 6 ) = 150
√
- The total surface area is:
SA= 150
√
3 +
1
2
( 6 )( 10 )( 22 )
= 150
√
3 + 660 ≈ 919. 81 units^2