Surface Area and Volume of 3-Dimensional Solids

In the triangular pyramid number of faces and number of edges are $a$ and $b$ respectively, then find the value of $\left(b-a\right)$.

What is hemisphere? Write its properties.

Define radius of the sphere? A solid sphere is cut into two equal hemispheres. What is the ratio of the surface area of one of the hemispheres to the surface area of the entire sphere before it was cut?

What will be the surface area of a right rectangular prism if length, width and height are $7 \mathrm{m}, 12 \mathrm{m}$ and $15 \mathrm{m}$ respectively?

 Samuel has given a cylinder of surface area $1728\pi {\mathrm{cm}}^2$. Find the height of the cylinder if the radius of the base of the circle is $24 \mathrm{cm}$.

Write the number of faces of a Hexagonal pyramid.

Write the number of edges of a Hexagonal pyramid.

A hollow sphere of internal and external radii $6 \mathrm{cm} \& 8 \mathrm{cm}$ respectively, is melted and recast into small cones of base radius $2 \mathrm{cm}$ and height $8 \mathrm{cm}$. Find the number of cones.

Palabora Mine, Phalaborwa, is a South African copper mine. A total of $4.1$ million tonnes of copper have been extracted from this mine. In the image shown, Dillon Marsh, a South African artist, has combined photography and computer imaging to visualize the total copper output of the mine. The copper sphere in the image is placed on the ground from which it was extracted, and represents a scale model of the copper removed from the mine. Find the radius of the copper sphere, given that $1 {\mathrm{m}}^3$ of copper weighs about $8930 \mathrm{kg}$.        [Enter the value to the nearest integer and excluding units]

A family is replacing the cylindrical hot water boiler of the house. They cannot change the height of the boiler but they can double its diameter. If the previous tank could hold $100$ litres, can we predict what the new tank will hold? What would happen if the diameter of the tank is tripled?

Calculate the volume of a cone with radius $2.1 \mathrm{cm}$ and height $7.3 \mathrm{cm}$.        [Enter the value excluding units and up to three significant figures]

Calculate the volume of a sphere with radius $2 \mathrm{cm}$ .        [Enter the value excluding units and up to three significant figures]

Calculate the volume of a cylinder with radius $3 \mathrm{cm}$ and height $23 \mathrm{cm}$.        [Enter the value excluding units and up to three significant figures]

The volume of a regular hexagonal prism is $2800 {\mathrm{cm}}^3$. The height of the prism is $14 \mathrm{cm}$. Find the side of the hexagonal base.       [Enter the value correct up to three significant figures and excluding units]

Nasim fills a measuring jug with $310 {\mathrm{cm}}^3$ of water. She pours the water into a cylindrical vase with radius $4 \mathrm{cm}$. Find the height of water.   [Enter the value correct up to three significant figures and excluding units]

A solid metal cylinder has the following dimensions. The cylinder is melted down into $2 \mathrm{cm}$ cubes. How many cubes can be made?

A ornament is made in the shape of a triangular prism. The ornament is made from mahogany, which has a density of $0.71 \mathrm{g}/{\mathrm{cm}}^3$. Calculate the mass of the ornament.   [Enter the value excluding units]

A swimming pool with the dimensions shown is filled with water. The cost to fill the pool is $\$0.15$ per cubic centimetre of water. Find the cost of filling the pool.

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?