Two cubes each of side 8 cm are joined end to end find the volume of resulting cuboid

Two cubes, each of side 4 cm are joined end to end. Find the surface area of the resulting cuboid.

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Solution:

We will find the length of the edge of each cube by using the formula for the volume of a cube = a3, where the length of the edge is 'a'.

As the cubes are joined end to end, they will appear as follows:

Using the formula for the surface area of a cuboid = 2(lb + bh + lh), where l, b, and h are length, breadth, and height respectively.

Let the length of the edge of each cube be 'a'

Therefore, volume of the cube = a3

Volume of the cube, a3 = 64 cm3

a3 = 64 cm3

a = ∛(64 cm3)

a = 4 cm

Therefore,

Length of the resulting cuboid, l = a = 4 cm

Breadth of the resulting cuboid, b = a = 4 cm

Height of the resulting cuboid, h = 2a = 2 × 4 cm = 8 cm

Surface area of the resulting cuboid = 2 (lb + bh + lh)

= 2 (4 cm × 4 cm + 4 cm × 8 cm + 4 cm × 8 cm)

= 2 (16 cm2 + 32 cm2 + 32 cm2)

= 2 × 80 cm2

= 160 cm2

Thus, the surface area of the resulting cuboid is 160 cm2.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 13

Video Solution:

2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.

NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.1 Question 1

Summary:

The surface area of the resulting cuboid if 2 cubes each of volume 64 cm3 are joined end to end is 160 cm2.

☛ Related Questions:

Text Solution

Solution : As is clear from the adjoining figure, the length of the resulting cuboid `=3xx8cm=24 cm` Its width =8cm and its height = 8cm i.e l=24 cm, b = 8 cm and h=8 cm The total surface area of the resulting cuboid `=2(lxxb+bxxh+hxxl)` `=2(24xx8+8xx8+8xx24)cm^(2)=896 cm^(2)` <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NTN_MATH_X_C13_S01_005_S01.png" width="80%">

Question 12 Volume Surface Area Cuboid Cube Exercise 21.4

Answer:

Given details are,

Volume of each cube = 512 cm3

Let length of edge of each cube be ‘a’ cm

So,

Edge, a3 = 512 a = 3√512

= 8cm

When these two cubes are joined end to end, a cuboid is formed.

Length of cuboid = 8+8 = 16 cm

Breadth = 8 cm Height = 8 cm

Surface area of resulting cuboid = 2 (lb + bh + hl)

= 2 (16×8 + 8×8 + 8×16)

= 2 (128 + 64 + 128)

= 2 (320)

= 640 cm2

∴ Surface area of resulting cuboid is 640cm2.

Video transcript

hello welcome to leader learning today we are going to see a question that is z upon 3 minus 1 equals to 5 minus 5 so we need to find the z value 0 upon 3 equals to minus 5 plus 1 0.3 equals to minus 4 z equals to 3 into minus 4 is that equals to minus 12 the final value of that is minus 12 i hope you understand this video thank you for watching this video

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Hint: Here we will first find the new length of the cuboid formed by adding the side of the cube. Then we will find the breadth and height of the cuboid formed which is equal to the side of the cube. Then we will use the formula of the volume of a cuboid and substitute all the values of the dimensions in the formula. We will solve it further to get the volume of the resulting cuboid.

Formula used:

We will use the formula of Volume of a cuboid \[ = {\rm{length}} \times {\rm{Breadth}} \times {\rm{Height}}\]

Complete Step by step Solution:

The side of the cubes is 8 cm.It is given that these cubes are joined end to end to form a cuboid.Firstly we will find the new length of the cuboid formed and new breadth and new height of the cuboid formed. Therefore, we getNew length of the cuboid formed \[ = 2 \times {\rm{side}}\]\[ \Rightarrow \] New length of the cuboid formed \[ = 2 \times 8 = 16cm\]We know that the breadth and height of the cuboid will remain the same. Therefore, we getNew breadth of the cuboid formed \[ = {\rm{side}} = 8cm\]New height of the cuboid formed \[ = {\rm{side}} = 8cm\]Now we will use the basic formula of the volume to find the volume of the cuboid. Therefore, we getVolume of the cuboid \[ = {\rm{length}} \times {\rm{Breadth}} \times {\rm{Height}}\]Now we will put the values in the equation, we get\[ \Rightarrow \] Volume of the cuboid \[ = 16 \times 8 \times 8\]Multiplying the terms, we get\[ \Rightarrow \] Volume of the cuboid \[ = 1024c{m^3}\]

Hence the volume of the resulting cuboid is equal to \[1024c{m^3}\]

Note:

We need to keep in mind that when one or more cubes are joined then it takes the shape of a cuboid. A Cube is a shape with six flat surfaces, eight vertices or corners, and twelve edges. The length of all these edges is equal to each other. Angles made by the two consecutive sides and the edges or sides are \[{\rm{90}}^\circ \]. The Cube is the most symmetric in all hexahedron shape objects.

As the shape becomes cuboid, we will use the formula of volume of a cuboid. Volume is the amount of space occupied by an object in three-dimensional space. Volume is measured in cubic units.