Find the volume and surface area of the following square pyramid. Round your answer to the nearest tenth.

 

Find the volume and surface area of the pentagonal pyramid. Round your answer to the nearest tenth.

In order to help reduce employees' stress levels and give them a place to get away from their office cubicle, Amazon has built three giant spheres in downtown Seattle, USA. Inside the spheres, the climate is very similar to that of Costa Rica, providing a nice break from the sometimes cold and rainy Seattle weather. The spheres also contain waterfalls, a river and tropical gardens. The largest sphere measures $40$ m in diameter. 

If the volume of space available in the largest sphere to the nearest tenth is $V {\text{m}}^3$ then find $V$. $(\text{Take} \pi =22/7)$

In order to help reduce employees' stress levels and give them a place to get away from their office cubicle, Amazon has built three giant spheres in downtown Seattle, USA. Inside the spheres, the climate is very similar to that of Costa Rica, providing a nice break from the sometimes cold and rainy Seattle weather. The spheres also contain waterfalls, a river and tropical gardens. The largest sphere measures $40$ m in diameter. 

If the spheres are covered in glass, If the area of glass needed to cover the largest sphere is $S {\text{m}}^2$ then find $S$. $(\text{Take} \pi =22/7)$

Airbags became widely used in cars in the 1980s and 1990s as a method of making them safer. Although seat belts had become a standard safety feature, injuries still  persisted as the driver and passengers impacted the inside of the car. Airbags are installed so that, in a crash, they will deploy and create a soft barrier between the driver/ passenger and the car and its windows. A car can have multiple airbags, each positioned to protect a specific passenger. The driver's airbag is located in the steering wheel of the car, and when fully inflated can be approximated by a cylinder. If the cylinder has a height of $25$ cm and a radius of $28$ cm, If the volume of air in the airbag when fully inflated is $V {\text{cm}}^3$ then find $V$.

Airbags became widely used in cars in the 1980s and 1990s as a method of making them safer. Although seat belts had become a standard safety feature, injuries still  persisted as the driver and passengers impacted the inside of the car. Airbags are installed so that, in a crash, they will deploy and create a soft barrier between the driver/ passenger and the car and its windows. A car can have multiple airbags, each positioned to protect a specific passenger. The driver's airbag is located in the steering wheel of the car, and when fully inflated can be approximated by a cylinder. If the cylinder has a height of $25$ cm and a radius of $28$ cm, If the amount of material required to make the airbag is $S {\text{cm}}^2$ then find $S$. (Take $\pi =22/7$) 

In order to solve problems of manoeuvrability and stability, inventor James Dyson inserted a ball into his vacuum cleaner design. The motor could be moved to fit inside the ball, which lowered the center of gravity and increased the stability of the machine. At the same time, the ball allows the machine to be turned around comers with ease. If the motor for a particular vacuum cleaner has a volume of $4200 {\text{cm}}^3$, if find the radius of the smallest ball that could be used to hold it is an integer $r$ cm then find $r$. $(\text{Take} \pi =22/7)$

Three-dimensional puzzles are popular toys for adolescents, especially since the Rubik's cube. The wooden puzzle shown here has only $10$ pieces but is very difficult to solve. The puzzle comes with the pieces arranged in the shape of a cube, and the aim is to rearrange them to make a square pyramid. If the puzzle contains $9 {\text{cm}}^3$ of wood, find the dimensions of the pyramid. 

The LifeStraw personal water filter removes $99.9999\%$ of waterborne bacteria. It can turn up to $1000$ liters of contaminated water into safe drinking water. If the length of the straw is $9$ inches and the diameter is $1$ inch, If the volume of water that the straw can hold is $V {\text{inches}}^3$ rounded of to the nearest hundredth, then find $V$. (Take $\pi =22/7$)