Three metal cubes with edges of 6cm, 8cm, and 10cm, respectively, are melted together and formed into a single cube. Find the surface area of the new cube.

The given values are

6 cm , 8 cm , 10 cm

Volume of cube

\$s^3\$

Now, plug these values into the formula

Cube1 = \$6^3\$ = 216

Cube2 = \$8^3\$ = 512

Cube3 = \$10^3\$ = 1000

Find the total volume of the three cubes

Total volume = 216 + 512 + 1000

After simplification

Total volume = 1728 cu.m

To find the edge length of the new cube that would have the same volume, take the cube root of the total volume

Edge length of the new cube = \$\sqrt 3("Total Volume")\$

Now, plug these values

Edge length of the new cube = \$\sqrt3(1728) = 12 cm\$

The surface area of a cube is

\$"Surface Area" = 6 times ("edge length")^2\$

Now, plug these values into the formula

\$"Surface area" = 6 times (12)^2\$

\$"Surface area" = 6 times 144\$

Surface area = 864 sq.cm

The surface area of the new cube is 864 sq.cm

Can you summarize what you’ve understood in the above steps?

Incorrect.This value is too low, as we calculated the surface area to be 864 sq cm

750 sq.cm

Incorrect.This value is too low, as we calculated the surface area to be 864 sq cm

800 sq.cm

This option is correct because it matches the calculated surface area of the new cube

864 sq.cm

Incorrect.This value is too low, as we calculated the surface area to be 864 sq cm

725 sq.cm

Option

C

Can you summarize what you’ve understood in the above steps?