The quadrilateral pyramid

The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.

Correct answer:

V =  10.24 dm3
S =  31.3831 dm2

Step-by-step explanation:

a=24 cm→ dm=24:10  dm=2.4 dm b=3.2 dm h=0.4 m→ dm=0.4⋅ 10  dm=4 dm  S1​=a⋅ b=2.4⋅ 3.2=25192​=7.68 dm2  V=31​⋅ S1​⋅ h=31​⋅ 25192​⋅ 4=25256​ dm3=10.24 dm3
s2​=h2+(a/2)2​=42+(2.4/2)2​≐4.1761 dm s3​=h2+(b/2)2​=42+(3.2/2)2​≐4.3081 dm  S2​=2a⋅ s3​​=22.4⋅ 4.3081​≐5.1698 dm2 S3​=2b⋅ s2​​=23.2⋅ 4.1761​≐6.6818 dm2  S=S1​+2⋅ S2​+2⋅ S3​=7.68+2⋅ 5.1698+2⋅ 6.6818=31.3831 dm2

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algebrasolid geometryplanimetricsUnits of physical quantities

 
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