Question

A rectangular sheet of dimensions 1.57 m × 4.16 m was brought to form an ice cream cone of radius 2.5 cm and height 6 cm. Then find out how many ice cream cones can be prepared from that?
A) 320
B) 1280
C) 640
D) 512

Answer 1

Hint: At first we have to find the area of the rectangular sheet dimensions 1.57 m × 4.16 m. Then the area of the conical ice cream for the given data. After that we need to divide the area of the conical ice cream with the rectangular sheet. The result will give the number of ice cream that can be prepared from that rectangular sheet.

Complete step-by-step solution:
Now we have to find the area of the rectangular sheet
$\begin{array}{c}{\rm{Area}}\;{\rm{of}}\;{\rm{the}}\;{\rm{rectangular}}\;{\rm{sheet}} = 1.57 \times 4.16\;{{\rm{m}}^2}\\\ = 6.5312\;{{\rm{m}}^2}\end{array}$
Converting meter into the centimeter = 65312 cm2

For calculating the area of the conical ice cream, we have to calculate the length of the surface. Since radius, height and length of the cone form a right angle triangle so we can use Pythagoran's theorem to calculate the length of the surface.
Let l be the length of the surface, h is the height and r is the radius of the cone.
$\begin{array}{c}{l^2} = {h^2} + {r^2}\\\ = \sqrt {{h^2} + {r^2}} \\\ = \sqrt {{6^2} + {{2.5}^2}} \\\ = 6.5\;{\rm{cm}}\end{array}$

${\rm{Area}}\;{\rm{of}}\;{\rm{the}}\;{\rm{surface}}\;{\rm{of}}\;{\rm{the}}\;{\rm{ice}}\;{\rm{cream}} = \pi rl$
Substituting π = 3.14, r = 2.5 cm, l = 6.5 in the above formula.
$\begin{array}{c}{\rm{Area}}\;{\rm{of}}\;{\rm{the}}\;{\rm{surface}}\;{\rm{of}}\;{\rm{the}}\;{\rm{ice}}\;{\rm{cream}} = 3.14 \times 2.5 \times 6.5\\\ = 51.05\;{\rm{c}}{{\rm{m}}^2}\end{array}$

Now, we have to divide the area of the rectangle with the area of the ice cream. It will give us the number of cones that can be prepared.
$\begin{array}{c}{\rm{Number}}\;{\rm{of}}\;{\rm{ice}}\;{\rm{cream}}\;{\rm{cone}} = \dfrac{{65312}}{{51.05}}\\\ = 1280\end{array}$

Hence, the correct option is B.

Note: Area of a rectangle can be calculated by multiplying the length and the breadth and the area of a cone can be calculated by multiplying π times of length with radius. Here, we have to determine the number of ice cream cones that can be prepared for the given data. So, by dividing the area of the rectangle with the area of the cone, it will give us the number of ice cream cones that can be made.