Three cubes each of volume 64`"cm"^3` are joined end to end to form a cuboid. Find the total surface area of the cuboid so formed?
Finding Side of Cube from Volume,
Given,
Volume of 1 cube = 64`"cm"^3`
⇒ `"Side"^3` = 64`"cm"^3`
⇒ `"a"^3` = 64`"cm"^3`
⇒ `"a"^3` = `4^3`
Surface area of cuboid
length of cuboid = a + a + a = 4 + 4 + 4 = 12 cm
Breadth = a = 4 cm
Height = a = 4 cm
Hence,
`l` = 12 cm, `b` = 4 cm, `h` = 4 cm
Area of Cuboid = 2 (`lb + bh + hl`)
= 2 (12`\times`4 + 4`\times`4 + 4`\times`12)
= 2 (48 + 16 + 48)
= 2 (112)
= 2`\times`112
= 224
Hence, Area of Cuboid = 224 `"cm"^2`