Question
Three cubes whose edges measure $3 cm, 4 cm$ and 5 cm respectively are melted to form a new cube. Find the surface area of the new cube formed.
✓
Answer
Three cubes of edges $3 cm, 4 cm$ and 5 cm are melted and molded to form a new cube.
i.e., volume of the new cube $=$ sum of the volumes of the three cubes
$=(3)^3+(4)^3+(5)^3 \\
=27+64+125 \\
=216 cm^3$
We have that volume of a cube $=(\text { side })^3$
$\Rightarrow 226=(\text { side })^3$
$\Rightarrow$ side of the new cube $=\sqrt[3]{216}=6 cm$
$\therefore$ Surface area of the new cube $=6 \times(\text { side })^3=6 \times(6)^2=216 cm^2$
i.e., volume of the new cube $=$ sum of the volumes of the three cubes
$=(3)^3+(4)^3+(5)^3 \\
=27+64+125 \\
=216 cm^3$
We have that volume of a cube $=(\text { side })^3$
$\Rightarrow 226=(\text { side })^3$
$\Rightarrow$ side of the new cube $=\sqrt[3]{216}=6 cm$
$\therefore$ Surface area of the new cube $=6 \times(\text { side })^3=6 \times(6)^2=216 cm^2$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angle.
Expand : $(7 x+m)^3$
→A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distances from the town at different times are shown by the given graph.
Study the above graph carefully and answer the questions given below:
Study the above graph carefully and answer the questions given below:
- What is the scale taken for the time-axis?
- How much time did the person take for the travel?
- How far is the place of the merchant from the town?
- Did the person stop on his way? Explain.
- During which period did the ride fastest?
A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively. How long will they to finish it they work together?
A cistern has two inlets A and B which can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes are opened together in the empty tank, how much time will they take to fill the tank completely?
Find the cost of $3\frac{2}{5}$ metres of cloth at $\text{Rs.}\ 63\frac{3}{4}$ per metre.
→Find the product:
$75\text{x}^2\text{y}\big(\frac{3}{5}\text{xy}^2+\frac{2}{5}\text{x}\big)$
→$75\text{x}^2\text{y}\big(\frac{3}{5}\text{xy}^2+\frac{2}{5}\text{x}\big)$
Add the following algebric expressions:
$\frac{7}{2}\text{x}^{3}-\frac{1}{2}\text{x}^{2}+\frac{5}{3},$$\frac{3}{2}\text{x}^{3}+\frac{7}{4}\text{x}^{2}-\text{x}+\frac{1}{3},$$\frac{3}{2}\text{x}^{2}-\frac{5}{2}\text{x}-2$
→$\frac{7}{2}\text{x}^{3}-\frac{1}{2}\text{x}^{2}+\frac{5}{3},$$\frac{3}{2}\text{x}^{3}+\frac{7}{4}\text{x}^{2}-\text{x}+\frac{1}{3},$$\frac{3}{2}\text{x}^{2}-\frac{5}{2}\text{x}-2$
Find the least number of 4 digits which is a perfect square.
A dealer gets Rs. 30 less if instead of selling a chair at a gain of 12% he sells it at a gain of 8%. Find the cost price of the chair.