Question

83. Base of a right pyramid is a square, length of diagonal of the base is 24V2 m. If the volume of the
pyramid is 1728 cu. m, its height is :​

Answer 1

Required Answer:

A right pyramid with base square is a Square pyramid whose volume can be calculated by:

$\huge{ \boxed{ \sf{V = \frac{1}{3} Ah}}}$

Where V is the volume,

A is the area of the square base

h is the height of the Square pyramid.

GiveN:

• Length of diagonal of base = 24√2 m
• Volume of pyramid = 1728 m³

To FinD:

• Height of the pyramid?

Step-by-step Explanation:

Area of the square base:

➛ diagonal² / 2 m²

➛ (24√2)² / 2 m²

➛ 24² × 2 / 2 m²

➛ 576 m²

Finding height by using Formula,

➛ 1/3 Ah = Volume

➛ 1/3 × 576 m² × h = 1728 m³

➛ 192h m² = 1728 m³

➛ h = 9 m

Hence,

The height of the square pyramid:

$\huge{ \boxed{ \sf{ \red{9 \: m}}}}$

Answer 2

$\underline{\underline{\sf{\clubsuit \:\:Question}}}$

• Base of a right pyramid is a square, length of diagonal of the base is 24√2 m. If the volume of the  pyramid is 1728 cu. m, it's height is

$\underline{\underline{\sf{\clubsuit \:\:Given}}}$

• Base of a right pyramid is a square

• Length of diagonal of the base = 24√2 m

• Volume of the  pyramid = 1728 cu. m

$\underline{\underline{\sf{\clubsuit \:\:To\:Find}}}$

• Height of pyramid

$\underline{\underline{\sf{\clubsuit \:\:Answer}}}$

• Height of the square pyramid is 9m

$\underline{\underline{\sf{\clubsuit \:\:Calculations}}}$

$\boxed{\sf{Volume\:\:of\;\:Pyramid\:\:=\:\:\dfrac{1}{3}\:\times\:Area\:of\:Base\:\times\:Height}}$

Area of the base = 1/2 × (Diagnol)²

Area of the base = 1/2 × (24√2 m)²

Area of the base = 1/2 × 24√2 m × 24√2 m

Area of the base = 1/2 × 1152 m²

Area of the base = 576 m²

Keeping the value in Volume of pyramid formula :

$\sf{Volume\:\:of\;\:Pyramid\:\:=\:\:\dfrac{1}{3}\:\times\:Area\:of\:Base\:\times\:Height}$

$\sf{Volume\:\:of\;\:Pyramid\:\:=\:\:\dfrac{1}{3}\:\times\:576\:m^2\:\times\:Height}$

$\sf{Volume\:\:of\;\:Pyramid\:\:=\:\:\dfrac{576}{3}\:m^2\:\times\:Height}$

$\sf{Volume\:\:of\;\:Pyramid\:\:=\:\:\ 192\:m^2\:\times\:Height}$

$\sf{1728\:m^3\:\:=\:\:\ 192\:m^2\:\times\:Height}$

$\sf{\dfrac{1728\:m^3}{{192\:m^2}}\:\:=\:\:\ \dfrac{192\:m^2\:\times\:Height}{192\:m^2}}$

$\sf{9m\:\:=\:\:Height}$

∴ Height of the square pyramid is 9m