Surface Area of a Cuboid

The length, breadth and height of a cuboid are in the ratio $3 : 4 : 6$ and its volume is $576 {\mathrm{cm}}^3$. Find the whole surface area of the cuboid.

The sum of length, breadth and height of a cuboid is $19 \mathrm{cm}$ and its diagonal is $11 \mathrm{cm}$. Find the surface area of the cuboid.

The paint in a certain container is sufficient to paint an area equal to$9.375 {\mathrm{m}}^2$. How many bricks of dimensions $22.5 \mathrm{cm}\times 10 \mathrm{cm}\times 7.5 \mathrm{cm}$ can be painted out of this container?

What are the dimensions (length, breadth and height respectively) of a cuboid with volume $720 {\mathrm{cm}}^3$ , surface area $484 {\mathrm{cm}}^2$ and the area of the base $72 {\mathrm{cm}}^2$?

The length of a room is $\frac{4}{3}$ times its breadth. The total area of the $4$ walls of this room is $\frac{28}{15}$ times the area of the floor of the room. What is the ratio between the height of the room to the length of room?

The sum of length, breadth and depth of a cuboid is $19 \mathrm{cm}$, and its diagonal is $5\sqrt{5} \mathrm{cm}$. Its surface area would be:

The sum of length, breadth and depth of a cuboid is $19 \mathrm{cm}$ and its diagonal is $5\sqrt{5} \mathrm{cm}$. What will be its surface area?

A room is $6\mathrm{m}$ long, $5 \mathrm{m}$ broad and $4 \mathrm{m}$ high. If all the walls are to be covered with paper $50 \mathrm{cm}$ wide, the length of the paper is:

The height of a room is $\frac{1}{4}$ of the sum of length and breadth and the cost of painting its walls at the rate of $50 \mathrm{p}$ per ${\mathrm{m}}^2$  is $₹400$. Find its height?

A cubical box has each edge $15 \mathrm{c}\mathrm{m}$ and another cuboidal box is having $l, b$and $h$ as $16.5 \mathrm{cm}, 12 \mathrm{cm},$and $7 \mathrm{c}\mathrm{m}$ respectively. Find out which box has the smaller total surface area.

The lateral surface area of a cube of side $12 \mathrm{cm}$ is

Find the lateral surface area of a cuboid with dimensions length $=3 \mathrm{cm}$, breadth $=2 \mathrm{cm}$ and height $=5 \mathrm{cm}$.

Find the lateral surface area of a cuboid with dimensions length $=2 \mathrm{m}$, breadth $=4 \mathrm{m}$ and height $=5 \mathrm{m}$.

A cubical box has each edge $10 \mathrm{cm}$ and another cuboidal box is $12.5 \mathrm{cm}$ long, $10 \mathrm{cm}$ wide and $8 \mathrm{cm}$ height. Which box has the greater lateral surface area and by how much?

A cubical box has each edge $10 \mathrm{cm}$ and another cuboidal box is $12.5 \mathrm{cm}$ long, $10 \mathrm{cm}$ wide and $8 \mathrm{cm}$ height. Which box has the greater lateral surface area and by how much?

A cubical box has each edge $10 \mathrm{cm}$ and another cuboidal box is $12.5 \mathrm{cm}$ long, $10 \mathrm{cm}$ wide and $8 \mathrm{cm}$ height. Which box has the smaller total surface area and by how much?

Swetha cake shop was placing an order for making cardboard boxes for packing their cakes. Two sizes of boxes were required. The bigger box of dimensions $25 \mathrm{cm}\times 20 \mathrm{cm}\times 5 \mathrm{cm}$ and the smaller box of dimensions $15 \mathrm{cm}\times 12 \mathrm{cm}\times 5 \mathrm{cm}$. For all the overlaps, $5\%$ of the total surface area is required extra. If the cost of the cardboard is $₹4$ for $1000 {\mathrm{cm}}^2$, find the cost of cardboard required for supplying $250$ boxes of each kind.

A cube with $3-\mathrm{inch}$ edges is to be constructed from $27$smaller cubes with$1-\mathrm{inch}$ edges. Twenty-one of the cubes are coloured red and $6$are coloured white. If the $3-\mathrm{inch}$ cube is constructed to have the smallest possible white surface area showing, then what fraction of the surface area is white?

Diagonal of a cuboid is$4\surd 3$ cm and the surface area equal to$96$ sq cm. Then
$$\begin{gathered} 1. l+b+h=12 \\ 2. l^2+b^2+h^2=lb+bh+hl \\ 3. l=b=h \end{gathered}$$
Codes:

The sum of the dimensions of a cuboid is$9 cm$ and the surface area is $45 cm$. Calculate the length of its diagonal.