Question

A sculpture is formed from a cylinder resting on top of a cuboid the cylinder has a radius of 40 cm and a height of 70cm. the cuboid measures 80cm by 80cm by 140cm. the sculpture is made of steel. the steel has a density of 8.05 g/cm^3 calculate the total mass of the sculpture in tonnes.

Answer 1

Given :

Radius of the cylinder = 40 cm

Height of the cylinder = 70 cm

Length of cuboid = 80 cm

Breadth of cuboid = 80 cm

Height of cuboid = 140 cm

Density of the steel  = 8.05 g per cubic cm

To Find :

What is the total mass of the sculpture in tonnes = ?

Solution :

The volume of the sculpture will be the sum of the cylinderical part and the cuboidal part , so :

Vol = vol of cylinder + vol of cuboid

Or, V=$\pi r^2 h + lbh$

        = $\pi \times 40^2 \times 70 + 80 \times 80\times 140$

        = 351680 + 896000

        = 1247680 $cm^3$

Since the density of the steel of which sculpture is made is given and we have find the vol , so the mass can be found by :

$density = \frac{mass}{volume}$

Or, $mass = density \times volume$

Or, $m = 8.05 \times 1247680$ g

So, m = 10043824 g

Since 1 tonn =1000 kg

So, 1 tonn = $1000 \times 1000 g$

Also , $1 g = \frac{1}{1000000} tonn$

So , $10043824 g = \frac{10043824 }{1000000}tonn$

                       = 10.04 tonns

Hence the total mass of the sculpture in tonnes is 10.04 tonnes .