# Find what is the Volume & Surface Area of Pyramid for L = 90, H = 30 & W = 75

The volume of pyramid is 67500 and surface area is 15128.354 for the given length as 90, height as 30 and width as 75, refer the calculation summary and work with steps for detailed explanation.

Calculation Summary | |
---|---|

Length | 90 in |

Width | 75 in |

Height | 30 in |

Volume V | 67500 in³ |

Surface Area | 15128.354 in² |

Lateral Area | 8378.354 in² |

## Work with Steps to find Volume & Surface Area of Pyramid for L = 90, H = 30 & W = 75

__Question:__

The length of pyramid is 90 inches, width is 75 inches and height is 30 inches, find what is the volume, surface area and lateral surface of the pyramid?

__Workout :__

step 1 Address the formula input parmaeter & values

Length = 90 in

Height = 30 in

Width = 75 in

step 2 Find Pyramid Volume using length, height and width values

Volume V = lwh/3

=90 x 75 x 30/3in³

= 202500/3in³

Volume v = 67500 in³

step 3 Find Surface Area using length, height and width values

Surface Area = lw + l √(w/2)² + h² + w √(l/2)² + h²

= (90 x 75) + 90 √(75/2)² + 30² + 75 √(90/2)² + 30² in²

= 6750 + 90 √(37.5)² + 30² + 75 √(45)² + 30² in²

= 6750 + 90 √(1406.25) + 900 + 75 √(2025) + 900 in²

= 6750 + 90 √2306.25 + 75 √2925 in²

= 6750 + (90 x 48.0234) + (75 x 54.0833) in²

= 8100 + 4322.1089 + 4056.2452 in²

Surface Area = 15128.354 in²

step 4 Find Lateral Area using length, height and width values

Lateral Area = l √(w/2)² + h² + w √(l/2)² + h²

= 90 √(75/2)² + 30² + 75 √(90/2)² + 30² in²

= 90 √(37.5)² + 30² + 75 √(45)² + 30² in²

= 90 √(1406.25) + 900 + 75 √(2025) + 900 in²

= 90 √2306.25 + 75 √2925 in²

= (90 x 48.0234) + (75 x 54.0833) in²

= 4322.1089 + 4056.2452 in²

Lateral Area = 8378.354 in²