Question

17. Kate and Harry went to a shop to buy two round
PIZZA of the same thickness but of different sizes.
The diameter of the smaller one is 28cm and the
cost is Rs. 140 and the larger one has a diameter
of 42cm which cost Rs.168.
Which PIZZA is cheaper? Explain.​

Answer 1

Answer:

The larger pizza is cheaper one than smaller pizza

Step-by-step explanation:

Given as :

Kate and Harry went to a shop to buy two round  pizza of the same thickness but of different sizes.

Let The thickness of both pizza = h cm

For smaller pizza

Diameter of smaller pizza = $d_1$ = 28 cm

So, Radius = $r_1$ =  $\dfrac{d_1}{2}$  = $\dfrac{28}{2}$

i.e   $r_1$ = 14 cm

Let thickness = $h_1$ cm

Now,

Volume of smaller pizza = $v_1$= π $r_1$² $h_1$

or, $v_1$= π (14)² h                  ............1

Cost of smaller pizza = Rs 140

 Again ,

For larger pizza

Diameter of larger pizza = $d_2$ = 42 cm

So, Radius = $r_2$ =  $\dfrac{d_2}{2}$  = $\dfrac{42}{2}$

i.e   $r_2$ = 21 cm

Let thickness = $h_2$ cm

Now,

Volume of larger pizza = $v_2$ = π $r_2$² $h_2$

or, $v_2$= π (21)² h                 ............2

The cost of larger pizza = Rs 168

Now,

The ratio of volume of larger pizza to smaller pizza

$\dfrac{volume of larger pizza}{volume of smaller pizza}$   =  $\dfrac{\pi21^{2} h }{\pi 14^{2}h }$

Or, $\dfrac{volume of larger pizza}{volume of smaller pizza}$ = [ $\dfrac{3}{2}$ ]²

∴  $\dfrac{volume of larger pizza}{volume of smaller pizza}$  = $\dfrac{9}{4}$                     .........3

Again

The ratio of cost of larger pizza to smaller pizza

$\dfrac{cost of larger pizza}{cost of smaller pizza}$ = $\dfrac{168}{140}$

∴   $\dfrac{cost of larger pizza}{cost of smaller pizza}$  = $\dfrac{6}{5}$                       .........4

Fronm eq 3 and eq 4

$\dfrac{9}{4}$  $>$ $\dfrac{6}{5}$

So, $\dfrac{volume of larger pizza}{volume of smaller pizza}$  $>$  $\dfrac{cost of larger pizza}{cost of smaller pizza}$

i,.e The larger pizza have greater value when compare to cost

∴ The larger pizza is cheaper one

Hence, The larger pizza is cheaper one than smaller pizza . Answer