Question

A birthday cake has two tiers as shown in the figure below . find the volume of the cake .

Answer 1

Hint: Remember to calculate the volume of the cake in a separate portion . The given figure has two cuboidal portions . So , we will use the formula for the volume cuboid which is \[Volume = l \times b \times h\] , where \[l,b,h\] are the length , breadth and height of the cuboid.

Complete step-by-step answer:
First we will calculate the area of the bottom part of the cake .
Given : Dimensions of bottom are as :
 \[length = 20cm\] , \[breadth = 20cm\] and \[height = 15cm\] .
Using the formula of volume of cuboid we get
\[Volume = l \times b \times h\] , putting the values of \[l,b,h\] we get ,
\[Volume = 20 \times 20 \times 15\] , on solving we get
\[Volume = 6000c{m^3}\].
Now we calculate the volume of upper portion of the cake
Given : dimensions of upper portion we get ,
\[length = 10cm\] , \[breadth = 10cm\] and \[height = 5cm\]
Using the formula of volume of cuboid we get
\[Volume = l \times b \times h\] , putting the values of \[l,b,h\] we get ,
\[Volume = 10 \times 10 \times 5\]
\[Volume = 500c{m^3}\] .
Now , the required volume can be calculated by adding the volume of the upper portion and bottom portion .
Therefore ,
 \[ = \left( {6000 + 500} \right)c{m^3}\]
\[ = 6500c{m^3}\]
Therefore , the volume of the cake is \[ = 6500c{m^3}\] .
So, the correct answer is “[\6500c{m^3}\]”.

Note: The dimensions of the object are given in \[cm\], therefore your final answer also should be in \[cm\] only which means the same dimensional units. Volume is the measurement of the amount of space inside a 3D object that can be filled . It can be the measurement of any solid objects like cube, square, cylinder, sphere, pyramid, etc. Volume of an object is usually measured using cubic units. By finding out the volume of an object it also helps us find the amount required to fill an object .