Download App

Mensuration – II (Volumes and Surface Areas of a Cuboid and a Cube) — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSMensuration – II (Volumes and Surface Areas of a Cuboid and a Cube)3 Marks
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 $=6 \times(\text { side })^3=6 \times(6)^2=216\ cm^2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Mensuration – II (Volumes and Surface Areas of a Cuboid and a Cube)→Mensuration – II (Volumes and Surface Areas of a Cuboid and a Cube) — all question types→MATHS STD 8 question papers→Gujarat Board STD 8 question papers→Gujarat Board question paper generator→

Similar questions

The sum of four consecutive numbers is 34. What are these numbers?
→
Find the area of a trapezium whose parallel sides are $38.7\ cm$ and $22.3\ cm$, and the distance between them is $16\ cm$.
→
Sonu buys $40\ kg$ of wheat at $Rs. 12.50/kg$ and $30\ kg$ of wheat at $Rs. 14/kg.$ At what rate $/kg$ should he sell the mixture to gain $5\%$ on the whole$?$
→
Find the cube root of each of the following natural numbers: $1157625$
→
If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4 ?
→
Express product as a monomials and verify the result for $x = 1, y = 2: \big(\frac{4}{9}\text{abc}^3\big)×\big(−\frac{27}{5}\text{a}^3\text{b}^2)×\big(−8\text{b}^3\text{c}\big)$
→
Of the four quadrilaterals square, rectangle, rhombus and trapezium one is somewhat different from the others because of its design. Find it and give justification.
→
Kusum buys some chocolates at the rate of Rs. $10$ per chocolate. She also buys an equal number of candies at the rate of Rs. $5$ per candy. She makes a $20\%$ profit on chocolates and $8%$ profit on candies. At the end of the day, all chocolates and candies are sold out and her profit is Rs. $240$. Find the number of chocolates purchased.
→
Solve the equation and check your result: $8x + 4 = 3(x – 1) + 7$
→
Pritam bought a plot of land for $Rs. 640000.$ Its value is increasing by $5\%$ of its previous value after every six months. What will be the value of the plot after $2$ years$?$
→