Cubes

Prince made a cuboid with the material Plasticine and with the dimensions $12 cm, 8 cm$ and $3 cm$. How many minimum numbers of such cuboids will be needed to form a cube?

Simplify ${\left(\frac{20+p}{30+6q}\right)}^3$

If the volume of a cube whose side is $25 \mathrm{cm}$ is k cm3, then find the value of $k$.

$$\begin{gathered} 2^3-1^3=1+2\times 1\times 3 \\ {3}^3-2^3=1+3\times 2\times 3 \\ {4}^3-3^3=1+4\times 3\times 3 \end{gathered}$$

Find the value of ${15}^3-{14}^3$ in the above pattern. 

$1^3=1=1$

$2^3=8=3+5$

$3^3=27=7+9+11$

Observe and continue this pattern to find the value of $7^3$ as the sum of consecutive odd numbers.

In a zoo, a tiger is kept in a $4.1 \mathrm{m}\times 4.1 \mathrm{m}\times 4.1 \mathrm{m}$ enclosure. Find the value of $\mathrm{k}$ in decimal form up to three decimal places, if volume of the enclosure is $\mathrm{k} {\mathrm{m}}^3$.

Find the smallest number by which $243$ must be multiplied to obtain a perfect cube.

A number when divided by $9$ gives the perfect cube of $6$ and when multiplied by $3$ gives another perfect cube of $18.$ What is the number?

What is the smallest perfect cube of three digits?

If the standard form of the cube of $\frac{-7}{11}$ is $\frac{-a}{b}$, then find the value of $a+b$.

Deepiksha has a cuboid of sides $15 \mathrm{cm}$, $30 \mathrm{cm}$ and $15 \mathrm{cm}$. How many such cuboids will she need to form a cube?( write the final answer in numerals)

Evaluate ${\left[\sqrt{{15}^2+8^2}\right]}^3$.

Difference of two perfect cubes is $189$. If the cube root of the smaller of the two numbers is $3$, find the cube root of the large number.

Atul made a cuboid of plasticine. Length, breadth and height of the cuboid are $25 \mathrm{cm}, 25 \mathrm{cm}$ and $50 \mathrm{cm}$. How many minimum such cuboids he needs to make a perfect cube?

The cube of a number $x$ is nine times of $x$, then find $x$ if $x\ne 0$ and $x\ne -3$.

To collect rainwater, Mini made a cubical tank that can hold $91125 {\mathrm{m}}^3$ water. She uses this water for watering the plants of her garden. If the height of the tank is $k \mathrm{cm}$, then find the value of $k$.

Find the value of ${\left[\begin{array}{c}{\left(\begin{array}{c}{24}^2+7^2\end{array}\right)}^{\frac{1}{2}}\end{array}\right]}^3$.

$(1+2+3{)}^3=$?

What is the value of $\sqrt[3]{-1}$.

Find the one's digit of the cube of each of the following numbers.

$77$