Volume of triangular prism = Base area x height
Problem 1 :
The height of a triangular prism is 6 cm and its base is an equilateral triangle of side 5 cm. Find the volume of the prism.
Solution :
Volume of triangular prism (V) = Base area x height
Base is in the shape of equilateral triangle,
Area of equilateral triangle = √3/4 × a²
Base area = √3/4 × 5² = √3/4 × 25 Base area = 6.25 √3 cm² |
Volume = A × h = 6.25 √3 × 6 = 37.5 √3 (√3 = 1.732) = 37.5 × 1.732 = 64.95 cm³ |
So, volume of triangular prism = 64.95 cm³
Problem 2 :
A right prism stands on a base which is a right triangle with legs 3 cm and 4 cm. find the volume of the prism if its height is 9 cm.
Solution :
Given, side a = 3 cm and b = 4 cm
Using Pythagoras theorem,
a² + b² = c² 3² + 4² = c² c = √(9 + 16) c = √25 c = 5 cm |
Perimeter of a triangle = (3 + 4 + 5) / 2 = 12/2 = 6 cm |
Area of triangle = √s(s - a)(s - b)(s - c)
= √6 (6 - 3)(6 - 4)(6 - 5)
= √6(3)(2)(1)
= √36
= 6 cm²
Volume of right prism = Base area × height
= 6 × 9
= 54 cm³
So, volume of triangular prism = 54 cm³
Problem 3:
The base of a right prism is a right triangle with legs 6 and 8 cm. if the volume of the prism be 192 cu cm. find the height of the prism.
Solution :
Side a = 6 cm and b = 8 cm
Using Pythagoras theorem
a² + b² = c² 6² + 8² = c² c = √(36 + 64) c = √100 c = 10 cm |
Perimeter of a triangle = (6 + 8 + 10) / 2
= 24/2
= 12 cm
Area of triangle = √s(s - a)(s - b)(s - c)
= √12 (12 - 6)(12 - 8)(12 - 10)
= √12(6)(4)(2)
= √576
= 24 cm²
Volume of right prism = Base area × height
192 = 24 × height
Height = 192/24
Height = 8 cm
So, height of triangular prism = 8 cm.
Problem 4:
The base of a right prism is a triangle with base 12 cm and height 6 cm. find the volume of the prism if its height is 7 cm.
Solution :
Given, base of the triangle = 12 cm
Height = 6 cm
Area base = 1/2 × 12 × 6
= 36 cm²
Height of the prism h = 7 cm
Volume of triangular prism V = A × h
= 36 × 7
V = 252 cm³
So, the volume of triangular prism V = 252 cm³
Problem 5 :
The height of a triangular prism is 8 cm and its base is an equilateral triangle of side 4 cm. Find the volume of the prism.
Solution :
Volume of triangular prism V = A × h
A = √3/4 × a² A = √3/4 × 4² A = √3/4 × 16 A = 4√3 cm² |
Volume = A × h = 4√3 × 8 = 32 √3 (√3 = 1.732) = 32 × 1.732 |
So, volume
of triangular prism = 55.42 cm³
Problem 6 :
The height of a right prism is 12 cm and its base is a triangle with 9 cm as base and height 5 cm. Find the volume of the prism.
Solution :
Base of the triangle prism = 9 cm
Height = 12 cm
Area base = 1/2 × 9 × 12
= 54 cm²
Height of the prism h = 5 cm
Volume of triangular prism V = A × h
= 54 × 5
V = 270 cm³
So, the volume of triangular prism V = 270 cm³
Problem 7 :
The base of a right prism is a right triangle with legs 12 and 5 cm. if the volume of the prism be 210 cu cm. find the height of the prism.
Solution :
Side a = 12 cm and b = 5 cm
Using Pythagoras theorem
a² + b² = c²
12² + 5² = c²
c = √(144 + 25)
c = √169
c = 13 cm
Perimeter of a triangle = (12 + 5 + 13) / 2
= 30/2
= 15 cm
Area of triangle = √ s(s - a)(s - b)(s - c)
= √ 15 (15 - 12)(15 - 5)(15 - 13)
= √ 15(3)(10)(2)
= √900
= 30 cm²
Volume of right prism = Base area × height
210 = 30 × height
Height = 210/30
Height = 7 cm
So, height of triangular prism = 7 cm.
Problem 8 :
A right prism base is a triangle whose sides are 6 cm, 8 cm and 10 cm. Find the volume of the prism if its height is 12 cm.
Solution :
side a = 6 cm and b = 8 cm and c = 10 cm
Perimeter of a triangle = (6 + 8 + 10) / 2
= 24/2
= 12 cm
Area of triangle = √s(s - a)(s - b)(s - c)
= √12 (12 - 6)(12 - 8)(12 - 10)
= √12(6)(4)(2)
= √576
= 24 cm²
Volume of right prism = Base area × height
= 24 × 12
V = 288 cm³
So, volume of the triangular prism = 288 cm³.
Problem 9 :
The height of a right prism is 15 m and its base is a triangle. If the volume of the prism is 187.5 cu m, find the area of the base triangle.
Solution :
Height of prism h = 15 m
Volume V = 187.5 cu m
Volume of triangular prism V = A × h
Area of base of triangular prism A = V/h
= 187.5/15
V = 12.5 m²
So, Area of base of triangle = 12.5 m²
Problem 10 :
A right prism is a triangle whose sides are 18 cm, 20 cm and 34 cm. find the volume of the prism if its height is 6 cm.
Solution :
Given, side a = 18 cm and b = 20 cm and c = 34 cm
Perimeter of a triangle = (18 + 20 + 34) / 2
= 72/2
= 36 cm
Area of triangle = √s(s - a)(s - b)(s - c)
= √36 (36 - 18)(36 - 20)(36 - 34)
= √36(18)(16)(2)
= √20736
= 144 cm²
Volume of right prism = Base area × height
= 144 × 6
V = 864 cm³
So, volume of the triangular prism = 864 cm³.
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