A right rectangular prism is a type of prism in which every lateral face is a rectangle. A right rectangular prism in general is referred to as as cuboids, or in simpler way as rectangular box.
Lateral Surface area of a rectangular prism: The area of lateral faces of a prism is known as lateral surface area.
Lateral surface area = perimeter * height
= (2l + 2w) * h
where, l = length of base
w = width of base
h = height
Total surface area of a rectangular prism:
Total surface area = Lateral surface area + 2*base
Volume of rectangular prism: The volume or capacity occupied by the rectangular prism. The volume of the rectangular prism is measured in cube units.
rectangular prism
Volume of the rectangular prism = L*B*H cube units
L is the length of the rectangular prism
B is the breadth of the rectangular prism
H is the height of the rectangular prism.
Model problem to find lateral surface area of the rectangular prism:
Ex 1:A right rectangular prism has a length of 5, width of 2, and the height of 3. Find the lateral area, total area and volume of the right rectangular prism.
Sol: Step 1: Given l = 5. w = 2, h = 3.
Step 2: Lateral area of right rectangular prism = perimeter * height
= (2l + 2w) * height
= [2(5) + 2(2)] (3)
= [10 + 4] * 3
Lateral area of right rectangular prism = 14 * 3 = 42.
Step 3 : Total area of right rectangular prism = Lateral area + 2* base
= Lateral area + 2* (length * width)
= 42 + 2* (5 * 2)
= 42 +20
Total area of right rectangular prism = 62.
Ex 2: A right rectangular prism has a length of 7 , width of 5, and the height of 6. Find the lateral area, total area and volume of the right rectangular prism.
Sol: Step 1: Given l = 7, w = 5, h = 6.
Step 2: Lateral area of right rectangular prism = perimeter * height
= (2l + 2w) * height
= [2(7) + 2(5)] (6)
= [14 + 10] * 6
Lateral area of right rectangular prism = 24 * 6 = 144.
Step 3: Total area of right rectangular prism = Lateral area + 2* base
= Lateral area + 2* (length * width)
= 144 + 2* (7 * 5)
= 144 + 2*35
Total area of right rectangular prism = 214.
Model problem to find the volume of the rectangular prism:
Ex 1: Finding the volume of the rectangular prism when the length is 7cm , breadth is 6cm and the height is 10 .
Sol:Step 1: Length of the rectangular prism = 7cm
Breadth of the rectangular prism = 6cm
Height of the rectangular prism = 10cm
Step 2: Volume of the rectangular prism = L*B*H cube. Units
= 7*6* 10
= 42*10
= 420 cm3
Volume of the rectangular prism is 420 cm3
Ex 2: Finding the volume of the rectangular prism when the length is 9cm, breadth is 8cm and the height is 12cm
Sol:Step 1:Length of the rectangular prism = 9cm
Breadth of the rectangular prism = 8cm
Height of the rectangular prism = 12cm
Step 2: Volume of the rectangular prism = L*B*H cube. Units
= 9*8* 12
= 72*12
= 864 cm3
Volume of the rectangular prism is 864 cm3
My forthcoming post is on free online math homework help and jee main 2013 sample paper will give you more understanding about Algebra.
Ex 3: Finding the volume of the rectangular prism when the length is5cm, breadth 4cm and the height is 6cm
Sol: Step 1: Length of the rectangular prism = 5cm
Breadth of the rectangular prism = 4cm
Height of the rectangular prism = 6cm
Step 2: Volume of the rectangular prism = L*B*H cube. Units
= 5*4* 6
= 20*6
= 120 cm3
Volume of the rectangular prism is 120 cm3
No comments:
Post a Comment