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WARRIOR [948]
3 years ago
8

this squared based pyramid is cut horizontally at a height of 15cm to leave this frustum base area=10cm

Mathematics
1 answer:
scoundrel [369]3 years ago
6 0

Answer:

583.33 cm³

Step-by-step explanation:

From the image attached, the total height (H) of the pyramid is 30 cm, the height of the frustrum (h) = 15 cm, the Frustrum base = lower base = B = 10 cm . To find the length of the upper base (b), we use:

\frac{b}{H-h}=\frac{B}{H}\\  b=(H-h)\frac{B}{H}\\b=(30-15)\frac{10}{30}=5\\b=5\ cm

The volume of the frustrum is given by:

V=\frac{1}{3}h(B_1+B_2+\sqrt{B_1B_2} )\\ Where\ B_1\ is \ the\ area \ of\ the\ upper\ base= 5cm*5cm=25cm^2\\B_1\ is \ the\ area \ of\ the\ lower\ base= 10cm*10cm=100cm^2\\V=\frac{1}{3}(10)(25+100+\sqrt{25*100} )=583.33\\V=583.33\ cm^3

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