Question

Lesson Posttest Question 5 Points 2 Two cubes each with a volume of 64 cm are joined end to end. Find the surface area of the resulting cuboid. O 110 cm2 O 120 cm2 O 140 cm2 O 160 cm2

Answer 1

Volume of two cubes each with 64 cm cube,

i.e. Volume first cube = Volume of second cube = 64 cm cube

The two cubes are joined together

Since The general formula for the Volume of cube is a³ where a is the dimension of the cube

So, with the given volume, we can determine the dimension of the cube

`\begin{gathered} \text{Volume = side}^3 \\ \text{Side}^3=Volume \\ a^3=64 \\ a=\sqrt[3]{64} \\ a=4\text{ cm} \end{gathered}`

Thus, the side of the cube is 4cm

Since when two cube combine then the resulting figure will be :

So, the Length of the resulting figure will be equal to the twice of the side of the cube

So,

Length = 4+4 = 8 cm

Breadth= 4cm

Height = 4cm

Since we have to formulate the surface of area of the cubiod

The mathematical expression for the surface area of cubiod is :

`\text{ Surface Area = 2(Length}* Breadth+Length* Height+Breadth* Height)`

Substitute the value and simplify

`\begin{gathered} \text{ Surface Area of cubiod= 2(8}*4+8*4+4*4) \\ S\text{urface Area of cubiod= 2(32}+32+16) \\ S\text{urface Area of cubiod= 2}*(80) \\ S\text{urface Area of cubiod= }160cm^2 \end{gathered}`

Answer : D) 160 cm²