Pyramid a+h

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

Correct result:

S =  2376.169 cm2
V =  6760 cm3

Solution:

a=26 cm v=3 10=30 cm S1=a2=262=676 cm2 h2=v2+(a/2)2=302+(26/2)21069 cm32.6956 cm S2=a h2/2=26 32.6956/213 1069 cm2425.0424 cm2 S=S1+4 S2=676+4 425.0424=2376.169 cm2a=26 \ \text{cm} \ \\ v=3 \cdot \ 10=30 \ \text{cm} \ \\ S_{1}=a^2=26^2=676 \ \text{cm}^2 \ \\ h_{2}=\sqrt{ v^2 + (a/2)^2 }=\sqrt{ 30^2 + (26/2)^2 } \doteq \sqrt{ 1069 } \ \text{cm} \doteq 32.6956 \ \text{cm} \ \\ S_{2}=a \cdot \ h_{2}/2=26 \cdot \ 32.6956/2 \doteq 13 \ \sqrt{ 1069 } \ \text{cm}^2 \doteq 425.0424 \ \text{cm}^2 \ \\ S=S_{1}+4 \cdot \ S_{2}=676+4 \cdot \ 425.0424=2376.169 \ \text{cm}^2
V=S1 v/3=676 30/3=6760 cm3



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