simple mathematical questions

Answer the following question [login to view URL] radius of the planet Neptune is 24600 km. Calculate the volume of the planet Neptune in km3. Give your answer in scientific notation and to 3 significant figures. Use π = 3.14. Note that this question is also testing your ability to write maths correctly, and so you may wish to re-read the information on the previous page before you attempt to input your answer. Q2. A detector at the North Pole picks up vibrations from an earthquake at the Equator. Assume that the radius of the Earth is 6300 km, and so a = 6300 km and b = 6300 km. The Earth is drawn as a circle with the North Pole marked at the top and the Equator drawn across the horizontal diameter. The radius from the centre to the North Pole is labelled a. The radius from the centre along the Equator to the right is labelled b. A right angled triangle is drawn with such that the right angle is at the dead centre of the circle and the hypotenuse, labelled c, joins lines a and b. Assuming for simplicity that these vibrations could travel in a straight line to reach the detector (in fact they will travel a curved path), what distance would they travel, i.e. the length of c? Give your answer in km, using scientific notation, and to 3 significant figures. The length of c is km, to 3 significant figures. Q3. The trunk of the tree makes a right angle with the ground, and the height of the tree is labelled H. A distance D from the base of the tree to a point on the ground. A triangle is drawn between the base of the tree, the top of the tree, and the point on the ground. The angle at the ground is labelled theta. You need to find the height of the tree in the image above. You know that θ = 28.2°. Suppose that D, the distance to the tree from the point at which the angle θ was measured, is 24.1 m. What is the height of the tree, H? Give your answer in metres, to three significant figures. (see image below) The height of the tree is  Answer m (to 3 significant figures) Q4.A pan of milk is heated until it boils and the pan is then removed from the heat source. As the milk cools, its temperature is recorded every 10 minutes. The axes for a graph of temperature against time of cooling have been chosen and labelled for you. Drag and drop the markers provided (or use the arrow keys on your keyboard) to plot the following three points on the graph: 1. A temperature of 100 °C after a time of 0 minutes; 2. A temperature of 66 °C after a time of 20 minutes; 3. A temperature of 38 °C after a time of 60 minutes. (y axis goes up 10. 20 , 30 ,40 etc) x axis goes in 10's also. Q5.n an experiment carried out on a fixed amount of gas held at constant volume, the pressure (in units of Pa) was measured as a function of the temperature (°C). A graph is plotted of the pressure of a gas against its temperature. The vertical axis is labelled 'pressure/10^5 Pa' and the horizontal axis is labelled 'temperature/°C'. The graph is a straight line passing through points which appear on the graph as follows: When the horizontal value is 0, the vertical value is 1.20. When the horizontal value is 80 the vertical value is 1.55. Calculate the gradient of the resulting graph to two significant figures, expressing your answer in scientific notation. gradient =  Pa/°C (see image below)