Question

Find the cost of a solid iron pyramid whose base is a square of side 2 cm and
height 12 cm at Rs 20 per cu cm.​

Answer 1

Answer:

(a) The perimeter of the base is P=4s, since it is a square, therefore,

P=4×6=24 cm

The general formula for the lateral surface area of a regular pyramid is LSA=

2

1

Pl where P represents the perimeter of the base and l is the slant height.

Since the perimeter of the pyramid is P=24 cm and the slant height is l=14 cm, therefore, the lateral surface area is:

LSA=

2

1

Pl=

2

1

×24×14=168 cm

2

Now, the area of the base B=s

2

with s=6 cm is:

B=s

2

=6

2

=36 cm

2

The general formula for the total surface area of a regular pyramid is TSA=

2

1

Pl+B where P represents the perimeter of the base, l is the slant height and B is the area of the base.

Since LSA=

2

1

Pl=168 cm

2

and area of the base is B=36 cm

2

, therefore, the total surface area is:

TSA=

2

1

Pl+B=168+36=204 cm

2

Hence, lateral surface area of the pyramid is 168 cm

2

and total surface area is 204 cm

2

.

(b) The perimeter of the base is P=4s, since it is a triangle, therefore,

P=3×12=36 cm

The general formula for the lateral surface area of a regular pyramid is LSA=

2

1

Pl where P represents the perimeter of the base and l is the slant height.

Since the perimeter of the pyramid is P=36 cm and the slant height is l=20 cm, therefore, the lateral surface area is:

LSA=

2

1

Pl=

2

1

×36×20=360 cm

2

Now, the area of the base B=

4

3

s

2

with s=12 cm is:

B=

4

3

s

2

=

4

3

×12×12=36

3

cm

2

The general formula for the total surface area of a regular pyramid is TSA=

2

1

Pl+B where P represents the perimeter of the base, l is the slant height and B is the area of the base.

Since LSA=

2

1

Pl=360 cm

2

and area of the base is B=36

3

cm

2

, therefore, the total surface area is:

TSA=

2

1

Pl+B=360+36

3

=36(10+

3

) cm

2

Hence, lateral surface area of the pyramid is 360 cm

2

and total surface area is 36(10+

3

) cm

2