Question

Find the volume of the composite solid. The base is an equilateral triangle.

Answer 1

Answer :

116√3/3 cubic inches

Note :

★ Area of equilateral triangle with side a is given as ; Area = √3a²/4 .

★ Volume of triangular base pyramid is given as ; Volume = (1/3) × A × H .

Where A is the area of triangle base and H is the height of pyramid .

★ Volume of triangular prism is given as ; Volume = A × H .

Where A is the area of triangular base and H is the height of prism .

Solution :

Here ,

The base of the given solid is an equilateral triangle of side 4 inches .

Thus ,

Area of base of given solid

= Area of equilateral triangle

= √3a²/4

= √3×4²/4 sq. inches

= 4√3 sq. inches

Clearly ,

The given solid is made by combining two different solids namely Pyramid and Prism .

Here ,

Height of Pyramid = 2 inches

Height of Prism = 9 inches

Thus ,

Volume of Pyramid

= (1/3) × Area of base × Height

= (1/3) × 4√3 × 2

= 8√3/3

Now ,

Volume of Prism

= Area of base × Height

= 4√3 × 9

= 36√3

Thus ,

The volume of the composite solid

= Volume of Pyramid + Volume of Prism

= 8√3/3 + 36√3

= (8√3 + 108√3)/3

= 116√3/3

Hence ,

Required answer is 116√3/3 cubic inches .