Mathematics
The adjoining figure shows a victory stand, each face is rectangular. All measurements are in centimetres. Find its volume and surface area (the bottom of the stand is open).
Mensuration
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Answer
By formula,
Volume of cuboid = l × b × h.
We know that,
Volume of part (3) = 50 × 40 × 12 = 24000 cm3
Volume of part (1) = 50 × 40 × (16 + 24)
= 50 × 40 × 40
= 80000 cm3.
Volume of part (2) = 50 × 40 × 24 = 48000 cm3.
So, the total volume = 24000 + 80000 + 48000 = 152000 cm3.
We know that
Total surface area = Area of front and back + Area of vertical faces + Area of top faces
Substituting the values we get,
= 2(50 × 12 + 50 × 40 + 50 × 24) cm2 + (12 × 40 + 28 × 40 + 16 × 40 + 24 × 40) cm2 + 3(50 × 40) cm2
= 2(600 + 2000 + 1200) cm2 + (480 + 1120 + 640 + 960) cm2 + (3 × 2000) cm2
= 2(3800) + 3200 + 6000 cm2
= 7600 + 3200 + 6000 cm2
= 16800 cm2.
Hence, volume = 152000 cm3 and surface area = 16800 cm2.
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