Advertisements
Advertisements
Question
Cubes A, B, C having edges 18 cm, 24 cm and 30 cm respectively are melted and moulded into a new cube D. Find the edge of the bigger cube D.
Advertisements
Solution
\[\text { We have the following: } \]
\[\text { Length of the edge of cube A = 18 cm }\]
\[\text { Length of the edge of cube B = 24 cm }\]
\[\text { Length of the edge of cube C = 30 cm }\]
\[\text { The given cubes are melted and moulded into a new cube D }. \]
\[\text { Hence, volume of cube D = volume of cube A + volume of cube B + volume of cube C }\]
\[ =\text { (side of cube A ) }^3 + \text { (side of cube B })^3 + \text { (side of cube C })^3 \]
\[ = {18}^3 + {24}^3 + {30}^3 \]
\[ = 5832 + 13824 + 27000\]
\[ = 46656 {cm}^3 \]
\[\text { Suppose that the edge of the new cube D = x }\]
\[ \Rightarrow x^3 = 46656\]
\[ \Rightarrow x = \sqrt[3]{46656} = 36 cm\]
\[ \therefore \text { The edge of the bigger cube D is 36 } cm .\]
APPEARS IN
RELATED QUESTIONS
What will happen to the volume of a cube, if its edge is trebled?
A cube A has side thrice as long as that of cube B. What is the ratio of the volume of cube A to that of cube B?
Fill in the blank in the following so as to make the statement true:
1 litre = ........ cu. cm
Find the surface area of a cube whose edge is 1.2 m.
Find the volume of a cube whose surface area is 96 cm2.
Side of a cube is 4.5 cm. Find the surface area of all vertical faces and total surface area of the cube.
The volume of a cube is 729 cm3. Find its total surface area.
The length of the diagonals of a cube is 8√3 cm.
Find its:
(i) edge
(ii) total surface area
(iii) Volume
A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes?
A river 2 m deep and 45 m wide is flowing at the rate of 3 km per hour. Find the amount of water in cubic metres that runs into the sea per minute.
