8.07 Volume of cylinders and spheres (Extended)
Find the volume of the following solids, rounding your answers to one decimal place:
Find the volume of a cylinder with radius 7 \text{ cm} and height 15 \text{ cm}, correct to two decimal places.
Find the volume of a cylinder, correct to one decimal place if:
Its radius is 6 \text{ cm} and height is 15 \text{ cm}.
Its diameter is 2 \text{ cm} and height is 19 \text{ cm}.
If the radius of a cylinder is 8 \text{ cm} and its height is 18 \text{ cm}, find the amount of water it can hold in litres. Round your answer to two decimal places.
Consider a cylinder with a diameter of 14 \text{ cm} and height of 10 \text{ cm}.
Find the volume of the cylinder in cubic centimetres, rounded to one decimal place.
State the capacity of the cylinder in millilitres, rounded to one decimal place.
Find the volume of the following spheres. Round your answers to two decimal places.
A student was calculating the volume of the sphere shown. The working is given below:
\begin{aligned} &\text{Step } 1 \, & V \, & = \, \dfrac{4}{3}\pi \times 9^3\\ &\text{Step } 2 \, & & = \, \dfrac{2916}{3}\pi\\ &\text{Step } 3 \, & & \approx \, 3053.63 \text{ cm}^3 \end{aligned}Explain what the student's mistake was, and find the actual volume of the sphere.
Find the volume of the following spheres. Round your answer to three decimal places.
A sphere with a radius of 5.8 \text{ mm}.
A sphere with a diameter of 17 \text{ cm}.
A sphere with a radius of 0.9 \text{ m}.
A sphere with a diameter of \dfrac{7}{8} \text{ cm}.
Jack's mother told him to drink 3 large bottles of water each day. She gave him a cylindrical bottle with height 17\text{ cm} and radius 5\text{ cm}.
Find the volume of the bottle. Round your answer to two decimal places.
Assuming that he drinks 3 full bottles as his mother suggested, calculate the volume of water Jack drinks each day. Round your answer to two decimal places.
If Jack follows this drinking routine for a week, how many litres of water would he drink altogether? Round your answer to the nearest litre.
A cylindrical tank with diameter of 3\text{ m} is placed in a 2 \text{ m} deep circular hole so that there is a gap of 40\text{ cm} between the side of the tank and the hole. The top of the tank is level with the ground.
Find the volume of dirt that was removed to make the hole. Give your answer to the nearest cubic metre.
Find the capacity of the tank to the nearest litre.
Approximately how many litres of water can this water cooler bottle contain? Round your answer to one decimal place.
There are two types of cylindrical soup cans available for Bob to purchase at his local store. The first has a diameter of 16 \text{ cm} and a height of 18 \text{ cm}, and the second has a diameter of 18 \text{ cm} and a height of 16 \text{ cm}.
State which type of can holds more soup, the first can or the second can.
A cylindrical swimming pool has a diameter of 5\text{ m} and a depth of 1.8\text{ m}.
How many litres of water can the pool contain? Round your answer to the nearest litre.
Express this amount of water in kilolitres.
Find the volume of a bowling ball with a radius of 10.9\text{ cm}. Round your answer to three decimal places.
How many whole lead balls with a diameter of 0.5 \text{ cm} can be made from the amount of lead in a ball with a diameter of 10 \text{ cm}?
Water in a cylindrical vase reaches a height of 22\text{ cm}. Bianca pours this water into a new spherical vase.
If both vases have a radius of 17\text{ cm}, how much space will be left empty in the spherical vase once the water is poured into it? Round your answer to two decimal places.
How many cubic centimetres of gas are necessary to inflate a spherical balloon to a diameter of 60 \text{ cm}? Round your answer to the nearest cubic centimetre.
The planet Jupiter has a radius of 69\,911\text{ km}, and planet Mercury has a radius of 2439.7\text{ km}. How many times bigger is the volume of Jupiter than Mercury? Assume that both planets are spheres. Round your answer to one decimal place.
The planet Mars has a radius of 3400 \text{ km}. What is the volume of Mars? Write your answer in scientific notation to three decimal places.
A cubic box has a volume of 34\,500 \text{ cm}^{3}.
Find the side length of the box, correct to 4 decimal places.
Using the answer from part (a), find the volume of the largest ball that can fit inside the box. Write your answer correct to the nearest \text{cm}^{3}.
Three spheres of radius 4\text{ cm} fit perfectly inside a cylindrical tube so that the height of the three spheres is equal to the height of the tube, and the width of each sphere equals the width of the tube:
Find the total volume of the three spheres. Round your answer to one decimal place.
Find the volume of the tube. Round your answer to one decimal place.
Calculate the percentage of the space inside the tube that is not taken up by the spheres. Round your answer to the nearest whole percent.
