Surface Area and Volume of Solids

Given the lateral surface area of the cube to be $900 {\mathrm{cm}}^2$, find the side of the cube in $\mathrm{cm}$.

Calculate the lateral surface area of a square pyramid if the side length of the base is $14$inches and the slant height of the pyramid is $20$inches. [Write the answer in ${\mathrm{in}}^2$]

The perimeter of the base of a triangular prism is $30 \mathrm{cm}$ and height of the triangular prism is $8 \mathrm{cm}$. What is the lateral surface area of the triangular prism?

The base of a triangular prism is $△\mathrm{ABC}$, where $\mathrm{AB}=3 \mathrm{cm}$, $\mathrm{BC}=4 \mathrm{cm}$ and $\angle \mathrm{B}=90°$. If the height of the prism is $10 \mathrm{cm}$. Find lateral surface area and total surface area.

A toy is in the shape of a square pyramid of base edge $16$ centimetres and slant height $10$ centimetres. What is the total cost of painting $500$ such toys, at $80$ rupees per square metre?

A square of side $5$ centimetres, and four isosceles triangles of base $5$ centimetres and height $8$ centimetres, are to be put together to make a square pyramid. How many square centimetres of paper is needed? 

A solid metallic hemisphere has diameter $42 \mathrm{cm}$. If the total cost of polishing the total surface at the rate $20$ paise per ${\mathrm{cm}}^2$ is $₹k$, then find the value of $k.$

A hollow hemispherical vessel has external and internal radius as $43 \mathrm{cm}$ and $42 \mathrm{cm}$, respectively. If cost of colouring it is $7$ paise per square centimetre, then find the cost of painting the vessel. Give the answer in $₹$ in decimal.

A hemispherical bowl of radius $9$ $\mathrm{cm}$ is full of liquid. The liquid is to be filled into cylindrical shaped bottle each of radius$1.5$ $\mathrm{cm}$ and height $4$ $\mathrm{cm}$. How many bottles are needed to empty the bowl?