The surface area of a solid spherical ball is $s {\mathrm{cm}}^2$. It is cut into $4$ identical pieces as shown below.

Find the total surface area of $4$ identical pieces of the solid spherical ball in term of $s$. Show your work.

Shown below is a small model of a cement mixer. The radius of the bottom of the drum is $5 \mathrm{cm}$ and that of the top of the drum is $2 \mathrm{cm}$.

Find the maximum quantity of cement, rounded to the nearest whole number, that the drum can hold. Show your steps. (Note: Take $\pi = \frac{22}{7}$)

A $5.54 \mathrm{l}$ watering can sprinkles water at the rate of $500 \mathrm{ml}/\min$, The can has a diameter of $14 \mathrm{cm}$ and is initially filled to its full capacity.

What is the height of water in the can after it is used for $8$ minutes? Show your work. (Note: Take $\pi = \frac{22}{7}$)

Two people have an equal amount of moulding clay. They make different solids of the same circular radius out of it- cylinder and hemisphere.

State true or false for the given statements and justify your answer.

1. Simran said, "The curved surface area of the cylinder is larger."
2. Manoj said, "Both the solids have the same curved surface area."

A bird feeder tube has a diameter of $8 \mathrm{cm}$ and height of $28 \mathrm{cm}$. The tube has $7$ circular openings of $2 \mathrm{cm}$ diameter each for the birds to eat from. The tube can hold a maximum of $3 \mathrm{kg}$ of bird food.

If the birds eat an average of $75 \mathrm{g}$ of food per hour, what will be the height of the food in the tube after $5$ hours? Show your work. (Note: Take $\pi = \frac{22}{7}$)

A semi-circular waffle sheet of radius $5 \mathrm{cm}$ is folded into an ice-cream cone as shown below.

Due to overlap while folding, the radius of the base of the cone is $80\%$ of what it would be without overlap. Find the approximate volume of the cone. Show your work. (Note: Take $\pi = \frac{22}{7}$)

A cloche is used to cover dishes before serving. Shown below is a hemispherical glass cloche of radius $13 \mathrm{cm}$. Kanan wants to use it to cover a cylindrical cake of volume $3168 {\mathrm{cm}}^3$.

Find one set of values of radius and height of the cake, such that the cloche does not touch the cake when covered. Show your steps. (Note: Take $\pi = \frac{22}{7}$.)

Shown below is a solid made of a cone, a cylinder and a hemisphere.

Prove that the total volume of the solid is twice the volume of the cylinder.

Dinesh is building a green house in his farm as shown below. The base of the greenhouse is circular having a diameter of $12 \mathrm{m}$ and it has a hemispherical dome on top.

How much will it cost him to cover the walls and top of the greenhouse with transparent plastic, if the plastic sheet costs $₹77$ per ${\mathrm{m}}^2$? Show your steps. (Note: Take $\pi = \frac{22}{7}$)