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).
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.
Related Questions
The lateral surface area of a cuboid is 224 cm2. Its height is 7 cm and the base is a square. Find
(i) a side of the square, and
(ii) the volume of the cuboid.
The external dimensions of an open rectangular wooden box are 98 cm by 84 cm by 77 cm. If the wood is 2 cm thick all around, find
(i) the capacity of the box
(ii) the volume of the wood used in making the box, and
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A cuboidal block of metal has dimensions 36 cm by 32 cm by 0.25 m. It is melted and recast into cubes with an edge of 4 cm.
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