Question

A cube has each of its faces covered by one face of an identical cube, making a solid. The volume of the solid is 875 What is the surface area of the solid?

Answer 1

Step-by-step explanation:

The solid is not shown, but anyone who ever rolled dice knows that a cube has 6 faces,

so attaching one cube to each face of the original cube,

we end up with a cluster of 1 + 6=7 cubes.

875 ÷ 7 = 125 , so if the solid volume is 875cm3

the volume of the each cube (the original cube and the other 6 identical ones) is

125cm3 .

Since the volume of a cube is the cube of the edge length,

the length of the edge of those cubes, in cm, is 3√125 = 5 .

The surface area of a face of a cube with edge length 5cm is

5cm × 5cm = 25cm2

In the 7 cube cluster, none of the 6 faces of the original cube is visible (all are covered).

The other 6 identical cubes attached to the original cube have one face covered (attached to the original cube,

so each one has 6-1=5 exposed faces.

The total exposed surface of the 7-cube cluster consists of

6 × 5=30 cube faces (5 faces from each of 6 cubes).

so, total surface area is 25 × 30 = 750cm2

Ans. 750cm2

Answer 2

The total surface area is 750 cm² when each face of a cube is covered by a face of a different cube, forming a solid.

Given that,

Each face of a cube is covered by a face of a different cube, forming a solid. The solid's volume is 875.

We have to find what is the solid's surface area.

We know that,

The cube has 6 faces,

So, attaching one cube to each face of the original cube,

1+6=7 cubes

If the solid volume is 875 cm³

Then $\frac{875}{7}$ = 125

The volume of the each cube is 125 cm³

The length of the cubes is $\sqrt[3]{125}$ = 5 cm

The surface area of the cube is 5×5 = 25 cm²

None of the original cube's six faces can be seen in the cluster of seven cubes.

Each of the other six similar cubes that are joined to the original cube has five faces that are exposed since each has one face covered.

The 7-cube cluster's total visible surface is made up of 65=30 cube faces.

The total surface area is 30×25 = 750 cm²

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