Question

The construction of leaning tower of Pisa began in August 1173 and finally completed

In 1372, taking 199 years. The building started tilting and arrest the tilt construction

And restoration work kept going for so long. The shape of minaret is cylindrical with

average height 56m ( approx) and outer radius 15.4m It has total of 296 steps.

The weight of entire tower is 14500 metric tonns.

Answer the following questions.

i) The volume of entire minaret in cu metre is :

a) 10435.04m3

b) 41740.16m3

c) 2608.76m3

d) 83480.32m3

ii) If it is decided to protect the entire building from rain during rainy seasons.

The amount of tarpaulin cloth required to cover the entire building is ----

a) 6166.16 sqm b) 6921.2 sqm c) 3455.76 sqm d) 6911.52 sqm

iii) The density ( mass/Volume) of entire building is kg/m3

is

a) 5558.20 kg/m3

b) 173.69 kg/m3

c) 1389.55 kg/m3

d) 347.39 kg/m3

iv) The cost of laminating all stairs @ 1050 per stairs is ----

a) 205800 b) 20580 c) 2058000 d) 2.0 million

v) Curved surface area of minaret is

a) 5420.8 m2

b) 2710.4 m2

c) 54208.0 m

2

d) 10841.6m2​

Answer 1

Given:

The shape of the minaret is cylindrical with an average height 56m ( approx) and outer radius 15.4m

It has a total of 296 steps.

The weight of the entire tower is 14500 metric tonnes.

To find:

The volume of the entire minaret in the cubic metre is?

If it is decided to protect the entire building from rain during rainy seasons. The amount of tarpaulin cloth required to cover the entire building is?

The density ( mass/Volume) of the entire building in kg/m3?

The cost of laminating all stairs @ 1050 per stairs is?

The curved surface area of the minaret is?

Solution:

Height of the minaret, h = 56 m

Radius of the minaret, r = 15.4 m

Finding the volume of the entire minaret:

∴ The volume of the entire minaret is,

= $\pi r^2 h$

= $\frac{22}{7} \times 15.4^2\times 56$

= $\boxed{\underline{\bold{41740.16\:m^3}}}$

Finding the amount of tarpaulin cloth required to cover the building:

∴ The amount of cloth required to cover will be,

= [CSA of the cylindrical minaret] + [Area of the top of the minaret]

= [$2\pi r h$] + [$\pi r^2$]

= $[2 \times \frac{22}{7} \times 15.4 \times 56] + [\frac{22}{7} \times 15.4^2]$

= $5420.8 + 745.36$

= $\boxed{\underline{\bold{6166.16\:m^2}}}$

Finding the density of the entire building in kg/m³:

The weight of the entire tower = 14500 metric tonnes = 14500 × 1000 = 14500000 kg

∴ The density of the entire building is,

= $\frac{Mass}{Volume}$

= $\frac{14500000}{41740.16}$

= $\boxed{\underline{\bold{347.38\:kg/m^3}}}$

Finding the cost of laminating all stairs:

The total no. of stairs in the minaret = 296

If the cost of laminating each stair is Rs. 1050

Then, the cost of laminating 296 stairs is = 296 × Rs. 1050 = $\boxed{\underline{\bold{Rs.\:310800}}}$

Finding the curved surface area of the minaret:

∴ The curved surface area of the minaret is,

= CSA of the cylinder

= $2\pi r h$

= $2 \times \frac{22}{7} \times 15.4 \times 56$

= $\boxed{\underline{\bold{5420.8 \:m^2}}}$

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