Question

18. Three metal cubes of sides 6 cm, 8 cm and 10 cm are melted and recast into a big cube. Find its total surface area.
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Answer 1

Answer:

TOTAL AREA OF CUBOID = 2(lb+bh+hl)

H= height. 8cm

H= height. 8cml= length. 6cm

H= height. 8cml= length. 6cmb=breath. 10cm

TSA= 2(6×10+10×8+8×6)

TSA= 2(6×10+10×8+8×6) 2×60+80+48

TSA= 2(6×10+10×8+8×6) 2×60+80+48 2×140+48

TSA= 2(6×10+10×8+8×6) 2×60+80+48 2×140+48 2×188

TSA= 2(6×10+10×8+8×6) 2×60+80+48 2×140+48 2×188 376

THE AREA OF CUBE IS 376 cm ²

Answer 2

Given:-

• Three cubes of different measures of sides.
• Side of Cube_1 = 6cm
• Side of Cube_2 = 8cm
• Side of Cube_3 = 1cm

To find:-

• Total Surface Area of big Cube = ?

Solution:-

We know that the volume of a cube is calculated by the formula a³ where, a is the side of the cube.

We also know that a big cube will be formed only when we join the volume of all three cubes.

So, the equation we get is

Volume of cube 1+Volume of cube 2+Volume of cube 3=Volume of bigger cube

So,

★»»6³+8³+10³=Volume of bigger cube.

Let the volume of bigger cube be x³.

»» 216+512+1000=x³

»»1728=x³

$\large\underline{\bf{»» \: \: \: \: \sqrt[3]{1728} = x}}$

»» 12cm=x

Henceforth the side of the bigger cube is 12cm.

Now we have to calculate the total surface area of the bigger cube.

We know that the formula for TSA of cube is 6a².Where,

• a = side of the cube

★ 6×12²=TSA of cube

»» 6×144=TSA of cube

»» 864cm²=TSA of cube.

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