Introduction about prism and cylinder:
Prism:
In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms
Cylinder:
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder.
(Source – Wikipedia)
Having problem with Find the Area of a Square keep reading my upcoming posts, i will try to help you.
Formula Used to Find the Surface Area of the Prism and Cylinder:
Rectangular prism:
Surface area of the rectangular prism (A) = 2(wh + lw + lh) square units
w – Width
h – Height
l – Length
Triangular prism:
Total Surface Area of the triangular prism (T.S.A)
T.S.A = L.S.A + 2 x Base Area
Total surface area T.S.A = (P x h + 2 A) sq. units
P - Perimeter
A - Area of the base
h - Height of the prism
Cylinder:
Surface area of cylinder (SA) = 2 p r^2 + 2 p r h square units
r – Radius
h – Height
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Surface Area of Prisms and Cylinders - Example Problems:
1. The rectangular prism has the length 25 cm, width 13cm and height 10 cm. find the surface area of the rectangular prism.
Solution:
Given:
Length (l) = 25 cm
Width (w) = 13 cm
Height (h) = 10 cm
Formula to find the surface area of the rectangular prism:
Surface area (A) = 2(wh + lw + lh) square units
= 2 (13 x 10 + 25 x 13 + 25 x 10)
= 2 (130 + 325 + 250)
= 2 (705)
= 1410
Surface area of the rectangular prism (A) = 1410 cm 2
2. The triangular prism has the base side length 3 cm, 4cm and 5 cm. its height is 10 cm. find total surface area of prism.
Solution:
Given:
Three side length of triangular prism = 3 cm, 4 cm, 5 cm
Height of the prism = 10 cm
Base of the triangle = 3 cm
Height of the triangle = 4 cm
The lateral surface area of the prism = p x h square units
= (3 + 4 + 5) x 10
=12x10
L.S.A =120 cm2
Now the area of the bases, A = 1/2 bh square units
h is the height of the triangle
= 1/2 x 3 x 4
A= 6 cm2
The total surface area of the prism = p h + 2 A square units
= 120 + 2 x 6
Total surface area of the prism = 1440 cm2
3. The cylinder has radius r = 3 cm, h= 12 cm. Find the surface area of cylinder.
Solution:
Given:
r= 3 cm
h=12 cm
Geometric Formula:
The surface area of the cylinder = 2 p r^2 + 2 p r h square units
= 2 x 3.14 x 32 + 2 x 3.14 x 3 x 12
= 56.52 + 226.08
The surface area of the cylinder = 282.6 cm2
Prism:
In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms
Cylinder:
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder.
(Source – Wikipedia)
Having problem with Find the Area of a Square keep reading my upcoming posts, i will try to help you.
Formula Used to Find the Surface Area of the Prism and Cylinder:
Rectangular prism:
Surface area of the rectangular prism (A) = 2(wh + lw + lh) square units
w – Width
h – Height
l – Length
Triangular prism:
Total Surface Area of the triangular prism (T.S.A)
T.S.A = L.S.A + 2 x Base Area
Total surface area T.S.A = (P x h + 2 A) sq. units
P - Perimeter
A - Area of the base
h - Height of the prism
Cylinder:
Surface area of cylinder (SA) = 2 p r^2 + 2 p r h square units
r – Radius
h – Height
Please express your views of this topic how to find answers to math problems by commenting on blog.
Surface Area of Prisms and Cylinders - Example Problems:
1. The rectangular prism has the length 25 cm, width 13cm and height 10 cm. find the surface area of the rectangular prism.
Solution:
Given:
Length (l) = 25 cm
Width (w) = 13 cm
Height (h) = 10 cm
Formula to find the surface area of the rectangular prism:
Surface area (A) = 2(wh + lw + lh) square units
= 2 (13 x 10 + 25 x 13 + 25 x 10)
= 2 (130 + 325 + 250)
= 2 (705)
= 1410
Surface area of the rectangular prism (A) = 1410 cm 2
2. The triangular prism has the base side length 3 cm, 4cm and 5 cm. its height is 10 cm. find total surface area of prism.
Solution:
Given:
Three side length of triangular prism = 3 cm, 4 cm, 5 cm
Height of the prism = 10 cm
Base of the triangle = 3 cm
Height of the triangle = 4 cm
The lateral surface area of the prism = p x h square units
= (3 + 4 + 5) x 10
=12x10
L.S.A =120 cm2
Now the area of the bases, A = 1/2 bh square units
h is the height of the triangle
= 1/2 x 3 x 4
A= 6 cm2
The total surface area of the prism = p h + 2 A square units
= 120 + 2 x 6
Total surface area of the prism = 1440 cm2
3. The cylinder has radius r = 3 cm, h= 12 cm. Find the surface area of cylinder.
Solution:
Given:
r= 3 cm
h=12 cm
Geometric Formula:
The surface area of the cylinder = 2 p r^2 + 2 p r h square units
= 2 x 3.14 x 32 + 2 x 3.14 x 3 x 12
= 56.52 + 226.08
The surface area of the cylinder = 282.6 cm2
