Question

The volume of a cube is 64cm).

a. Find the surface area of this cube.

b. Find the area of a section formed by the diagonals of the two opposite sides of this cube. Reason why this section can never be a square.

Answer 1

Step-by-step explanation:

b. i can understand

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Answer 2

${\bigstar}$ QUESTION${\bigstar}$

The volume of a cube is 64cm.

a. Find the surface area of this cube.

b. Find the area of a section formed by the diagonals of the two opposite sides of this cube. Reason why this section can never be a square.

${\bigstar}$ SOLUTION${\bigstar}$

☞volume of the cube = 64 cm

☞a³ = 64cm

☞$\boxed{\sf{ 4cm }}$

therefore ,

the length of the side of the cube is 4cm

${\bigstar}$TO FIND${\bigstar}$

• surface area of cube
• area of cross section formed my diagonals of the cube.

a)

☞surface area of the cube = 6a² sq units

☞6a² cm²

☞6(4)² cm²

☞6(16) cm²

☞$\boxed{\sf{ 96cm² }}$

b)

As the cross section is in rectangular form since opposite sides are equal,

☞area of the cross section

☞length × breadth

☞(diagonals of opposite sides) × (side of the cube)

➤diagonal of a side = √2 a = 4√2 cm

therefore ,

☞area of cross section

☞(4√2) × (4)

☞$\boxed{\sf{ 16√2 cm² }}$

As all the sides of the cross section are not equal ,they never be a square .

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CUBE:

TSA = 6a² sq .units

CSA = 4a² sq .units

volume = a³ cu.units