Activity › Discussion › Math › CLASS 8 Mensuration

CLASS 8 Mensuration
Posted by Alok on June 23, 2023 at 4:54 pmQuestion: The length, width, and height of a rectangular prism are 8 cm, 5 cm, and 3 cm respectively. Calculate its volume and total surface area.
Punith replied 3 months ago 3 Members · 2 Replies 
2 Replies

::
Given : – The length of the rectangular prism is , l = 8 cm.
The width of the rectangular prism is , w = 5 cm.
The height of the rectangular prism is, h= 3 cm.
Find : Volume of a rectangular prism, V = ?
Total Surface Area of a rectangular prism, TSA = ?
Calculation :
Now,
Volume of a rectangular prism, V = l × w × h
V = 8 × 5 × 3
V = 120 cm³
Total Surface Area , TSA = 2(lw + wh + lh)
TSA = 2(8×5 + 5×3 + 8×3)
TSA = 2(40 + 15 + 24)
TSA = 2(79)
TSA = 2 × 79
TSA = 158 cm²
Hence , The Volume of Rectangular Prism is 120 cm³ and The Total Surface Area is 158 cm².

::
To calculate the volume of a rectangular prism, you multiply its length, width, and height. Similarly, to find the total surface area, you need to calculate the sum of the areas of all its faces. Let’s calculate them step by step:
Volume:
The formula for volume is V = length × width × height.
Given:
Length = 8 cm
Width = 5 cm
Height = 3 cm
V = 8 cm × 5 cm × 3 cm
V = 120 cm³
Therefore, the volume of the rectangular prism is 120 cubic centimeters (cm³).
Total Surface Area:
The formula for the total surface area is A = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
Given:
Length = 8 cm
Width = 5 cm
Height = 3 cm
A = 2(8 cm × 5 cm) + 2(8 cm × 3 cm) + 2(5 cm × 3 cm)
A = 2(40 cm²) + 2(24 cm²) + 2(15 cm²)
A = 80 cm² + 48 cm² + 30 cm²
A = 158 cm²
Therefore, the total surface area of the rectangular prism is 158 square centimeters (cm²).
So, the volume of the rectangular prism is 120 cm³, and the total surface area is 158 cm².