External Dimensions Of A Wooden Cuboid Are 30 Cm\Xd725cm\Xd720cm If The Thickness Of The Wood Is 2cm All Around Find The Volume Of The Wood Contained

external dimensions of a wooden cuboid are 30 cm×25cm×20cm if the thickness of the wood is 2cm all around find the Volume of the wood contained inthe cuboid formed

Answer:

volume of the wood is 6,264cm^3

Step-by-step explanation:

A CUBOID is a solid figure which is similarly close to a cube. That is, a cube has a length, a width, and a height equal, but the cuboid does not.

How do we get the volume of a cuboid?

We solve it by just using the very common formula in finding for the volume of the cube

Vcube = s x s x s

Vcube = s^3

But since a cuboid may have different length, width, and height, then we have the VOLUME OF THE CUBOID

Vcuboid = L x W x H

In the given problem, we have a cuboid with a thickness. In finding for the volume that the cuboid can contain, all we have to do is subtract the outer dimensions of the cuboid by 2 cm.

Now let us find inner dimensions of the cuboid using 30cm as length, 25cm as width, and 20cm as height. Refer to the illustration provided for better understanding.

L inner = 30cm - (2)(2cm) = 26cm

W inner = 25cm - (2)(2cm) = 21cm

H inner = 20cm - (2)(2cm) = 16cm

Notice that we all have deducted 4cm in every dimension. Why? That is, since the problem did not state if the cuboid is to be covered on top, then we assume that it is covered. So, if we are to draw the top, front and side view of the cuboid, we will eventually notice that the inner dimensions will be 4cm lesser than the outer ones.

Thus, the volume that the cuboid can contain is

Vcontain = (26cm)(21cm)(16cm)

Vcontain = 8,736 cm^3

However, the problem asks for the volume of the wood in the form of the cuboid. So basically, we just need to find the volume of the container. We just need to subtract the inner volume from the outer volume. So we have

Vouter = 30cm x 25cm x 20cm

Vouter = 15,000 cm^3

Vwood = Vouter - Vinner

Vwood = 15,000cm^3 - 8736cm^3

Vwood = 6,264cm^3

Therefore, the A CUBOID is a solid figure which is similarly close to a cube. That is, a cube has a length, a width, and a height equal, but the cuboid does not.