Question

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Answer 1

Question :

• Q.1, The diagonals of a rhombus are of lengths 16 cm and 30 cm. Find it's area.

• Q.2, The total surface area of a cube is 96 cm². Find its volume.

Answer :

Q.1)

• The area of the rhombus is 240 cm².

Q.2)

• Volume of the cube is 64 cm³.

Explanation :

Given :

Q.1)

• Diagonal of the rhombus, a = 16 cm
• Diagonal of the rhombus, b = 30 cm

Q.2)

• Total surface area of the cube, T.S.A. = 96 cm²

To find :

Q.1)

• Area of the rhombus, A = ?

Q.2)

• Volume of the cube, V = ?

Knowledge required :

Q.1)

• Formula for area of a rhombus :

⠀⠀⠀⠀⠀⠀⠀⠀⠀A = ½ab

[Where : A = Area of the rhombus; a & b = Diagonals of the rhombus]

Q.2)

• Formula for total surface area of a cube :

⠀⠀⠀⠀⠀⠀⠀⠀⠀T.S.A. = 6(a)²

[Where : T.S.A = Total surface area of the cube; a = Equal side of the cube]

• Formula for volume of a cube :

⠀⠀⠀⠀⠀⠀⠀⠀⠀V = a³

[Where : V = Volume of the cube; a = Equal side of the cube]

Solution :

Q.1)

Area of the rhombus :

By using the formula for area of a rhombus and substituting the values in it, we get :

⠀⠀=> A = ½ab

⠀⠀=> A = ½ × 16 × 30

⠀⠀=> A = ½ × 480

⠀⠀=> A = 240

⠀⠀⠀⠀⠀⠀⠀∴ A = 240 cm²

Therefore,

• Area of the rhombus is 240 cm²

Q.2)

First let us find the equal side of the cube :

By using the formula for T.S.A. of a cube and substituting the values in it, we get :

⠀⠀=> T.S.A. = 6(a)²

⠀⠀=> 96 = 6(a)²

⠀⠀=> 96/6 = a²

⠀⠀=> 16 = a²

⠀⠀=> √16 = a

⠀⠀=> 4 = a

⠀⠀⠀⠀⠀⠀⠀∴ a = 4 m

Hence the equal side of the cube is 4 m.

Now,

To find the volume of the cube :

By using the formula for volume of a cube and substituting the values in it, we get :

⠀⠀=> V = a³

⠀⠀=> V = 4³

⠀⠀=> V = 64

⠀⠀⠀⠀⠀⠀⠀∴ V = 64 m³

Therefore,

• Volume of the cube, V = 64 cm³.

Answer 2

Hello !

Question 1:-

• The diagonals of. a rombus are of lengths 16cm and 30cm. Find its are

Given:-

• Diagonal 1 = 16cm
• Diagonal 2 = 30cm.

To find:-

• Area of the Rombus.

By using formula:-

$\huge \fbox \blue{Area=½d1×d2}$

Solution:-

Area = ½×16×30

$\implies$ 8× 30 = 240 cm²

Question 2:-

• The total surface area of a cube is 96m². Find its Volume.

Given:-

• T.S.A of cube = 96 m²

To find :-

• Volume of the cube.

First, we'll find the Side of this cube by using the formula :-

$\huge \fbox \blue{T.S.A=6a²}$

Substituting the values in the formula:-

96 = 6a²

$\implies$ 96/6 = a²

$\implies$ 16 = a²

$\implies$ √16 = a = 4m.

Finding Volume by formula

$\huge \fbox \blue{v=a³}$

v = 4³

v = 64 m³