9.06 Spheres
For each of the following spheres, find the following to two decimal places:
The surface area.
The volume.
A student was calculating the volume of the sphere shown.
The working is given below.
\begin{aligned} &\text{Step } 1 \quad & V \quad & = \quad \dfrac{4}{3}\pi \times 5^3\\ &\text{Step } 2 \quad & & = \quad \dfrac{500}{3}\pi\\ &\text{Step } 3 \quad & & \approx \quad 523.60 \text{ mm}^3 \end{aligned}State whether the following statements are true or false about the student's working.
The student's answer is correct.
The student found the volume for a hemisphere, not a sphere.
The student made a mistake by substituting the diameter for the radius.
The student made a mistake evaluating the power.
Find the radius of the sphere, correct to two decimal places:
A sphere has a surface area of 370\text{ cm}^2.
A ball has a surface area of 2463.01\text{ mm}^2.
Find the radius of the following spheres, correct to two decimal places:
A sphere has a volume of 200 \text{ cm}^3.
A sphere has a volume of \dfrac{512 \pi}{3} \text{ cm}^3.
By what factor will the volume increase if the radius of a sphere doubled?
Consider the following solid hemisphere:
Find the area of the curved surface of the dome, correct to three decimal places.
Find the area of the circular base of the hemisphere, correct to three decimal places.
Hence, find the total surface area of the hemisphere, correct to two decimal places.
Find the total surface area of the following hemispheres. Round your answer to three decimal places.
Find the volume of the following hemispheres. Round your answers to three decimal places.
Three spheres of radius 5\text{ cm} fit perfectly inside a tube so that the height of the three spheres is equal to the height of the tube, and each ball touches the cylinder wall.
Find the volume of the three spheres, correct to one decimal place.
Find the volume of the cylinder, correct to one decimal place.
Calculate the percentage of the tube that is not filled. Round your answer to the nearest whole number percentage.
The radius of a softball ball is 9.6\text{ cm}. Find the surface area of the ball, correct to three decimal places.
The planet Neptune has a radius of 24\,620 \text{ km}. Find the surface area of Neptune, correct to the nearest whole \text{km}^2.
The radius of a basketball ball is 24.1\text{ cm}. Find the volume, correct to three decimal places.
The planet Mars has a radius of 3400\text{ km}. Find the volume of Mars. Express your answer in scientific notation to three decimal places.
The planet Jupiter has a radius of 69\,911\text{ km}, and planet Venus has a radius of 6051.8\text{ km}.
Assume that both planets are spherical. How many times bigger is the volume of Jupiter than Venus? Round your answer to one decimal place.
The planet Neptune has a radius of 24\,622\text{ km}, and planet Earth has a radius of 6371\text{ km}.
Assume that both planets are spherical. How many times bigger is the surface area of Neptune than Earth? Round your answer to one decimal place.
Isabelle pours all of the water from a cylindrical vase into a spherical vase. Both vases have a radius of 16\text{ cm}. The water in the cylindrical vase reaches a height of 19\text{ cm}.
Will the water overflow when poured into the spherical vase?
How much remaining space will their be in the sperical vase, if any?
Assuming there is negligible wastage, how many whole lead balls with a diameter of 0.4\text{ cm} can be cast out of a lead ball with a diameter of 6\text{ cm}?
A lead bar with length of 3\text{ cm}, width of 2\text{ cm}, and thickness of 1\text{ cm} is melted down and made into 25 equally sized balls. Find the radius of each ball in centimetres, correct to two decimal places.
How many cubic centimetres of gas are necessary to inflate a spherical balloon to a diameter of 70\text{ cm}? Round your answer to the nearest cubic centimetre.
Copper weighs approximately 9 grams per cubic centimetre. Find the weight of 7 solid spheres of copper having a diameter of 16\text{ cm}. Round your answer to the nearest gram.