The base of a right pyramid is an equilateral triangle whose side is 8

1.	The base of a right pyramid is an equilateral triangle whose side is 8 cm. If the volume of the pyramid is 96 cm3, find the height of the pyramid?1. 8√3 cm2. 6√3 cm3. 6 cm4. 4√3 cm
Answer» Correct Answer - Option 2 : 6√3 cm Given: Side of Base triangle = 8 cm Volume of pyramid = 96 cm³ Concept: Using the formula of volume of the pyramid, calculate the height. Formula used: Volume of pyramid = (1/3) × (Area of base) × height Area of equilateral triangle = (√3/4) × (side)² Calculation: Let, the Height of the pyramid = ‘x’ Area of equilateral triangular base = (√3/4) × 8 × 8 = 16√3 cm² ∴ Volume of pyramid = (1/3) × (Area of base) × height ⇒ 96 = (1/3) × 16√3 × x ⇒ x = (96 × 3)/16√3 ⇒ x = 18/√3 cm ⇒ x = 6√3 cm

The base of a right pyramid is an equilateral triangle whose side is 8 cm. If the volume of the pyramid is 96 cm3, find the height of the pyramid?1. 8√3 cm2. 6√3 cm3. 6 cm4. 4√3 cm

Answer» Correct Answer - Option 2 : 6√3 cm

Given:

Side of Base triangle = 8 cm

Volume of pyramid = 96 cm³

Concept:

Using the formula of volume of the pyramid, calculate the height.

Formula used:

Volume of pyramid = (1/3) × (Area of base) × height

Area of equilateral triangle = (√3/4) × (side)²

Calculation:

Let, the Height of the pyramid = ‘x’

Area of equilateral triangular base = (√3/4) × 8 × 8

= 16√3 cm²

∴ Volume of pyramid = (1/3) × (Area of base) × height

⇒ 96 = (1/3) × 16√3 × x

⇒ x = (96 × 3)/16√3

⇒ x = 18/√3 cm

⇒ x = 6√3 cm

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