Surface Area of a Cuboid and a Cube

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

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

A wooden bookshelf has external dimensions as follows: height$= 110 \mathrm{cm}$, depth $= 25 \mathrm{cm}$, breadth $= 85 \mathrm{cm}$. The thickness of the plank is$5 \mathrm{cm}$ everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is $20 \mathrm{paise}$ per${\mathrm{cm}}^2$ and the rate of painting is $10 \mathrm{paise}$ per ${\mathrm{cm}}^2$ find the total expenses required for polishing and painting the surface of the bookshelf. [ write only numerical value without rupee symbol]

Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, and $k {\mathrm{cm}}^2$  tarpaulin would be required to make the shelter of height $2.5 \mathrm{m},$ with base dimensions $4 \mathrm{m}\times 3 \mathrm{m}$, then find $k$.

Shanti sweets stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions $25 \mathrm{c}\mathrm{m}\times 20 \mathrm{c}\mathrm{m}\times 5 \mathrm{c}\mathrm{m}$ and the smaller of dimensions $15 \mathrm{c}\mathrm{m}\times 12 \mathrm{c}\mathrm{m}\times 5 \mathrm{c}\mathrm{m}.$ For all the overlaps, $5\%$ of the total surface area is required extra. The cost of the cardboard is $\mathrm{₹}4$ for $1000 \mathrm{c}{\mathrm{m}}^2$. If the cost of cardboard required for supplying $250$ boxes of each kind is $₹k$, then find the value of $k$.

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is $30 \mathrm{c}\mathrm{m}$ long, $25 \mathrm{c}\mathrm{m}$ wide and $25 \mathrm{c}\mathrm{m}$ high. How much of tape $\left(\mathrm{in} \mathrm{cm}\right)$ is needed for all the $12$ edges?

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is $30 \mathrm{c}\mathrm{m}$ long, $25 \mathrm{c}\mathrm{m}$ wide and $25 \mathrm{c}\mathrm{m}$ high. If the area of the glass is $k {\mathrm{cm}}^2$, find $k$,

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

The floor of a rectangular hall has a perimeter $250 \mathrm{m}$. The cost of painting the four walls at the rate of $\mathrm{₹}10$ $\mathrm{per} {\mathrm{m}}^2$ is $\mathrm{₹} 15000$. If the height of the hall is $k \mathrm{m}$ then find $k$.

The length, breadth, and height of a room are $5 \mathrm{m}$, $4 \mathrm{m}$ and $3 \mathrm{m}$ respectively. If the cost of whitewashing the walls of the room and the ceiling at the rate of $\mathrm{₹} 7.50$ $\mathrm{per} {\mathrm{m}}^2$ is $\mathrm{₹}k$, find the value of $k$.

A plastic box $1.5 \mathrm{m}$ long, $1.25 \mathrm{m}$ wide and $65 \mathrm{c}\mathrm{m}$ deep, is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine the cost of sheet for the area of the box, if a sheet measuring $1 {\mathrm{m}}^2$ costs $\mathrm{₹}20$.

A plastic box $1.5 \mathrm{m}$ long, $1.25 \mathrm{m}$ wide and $65 \mathrm{c}\mathrm{m}$ deep, is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, if the area of the sheet required for making the box is $k {\mathrm{m}}^2$, then find the value of $k$.