Suppose a snowball is rolling down a hill, and its radius r is growing at a rate of 1 inch per minute. The volume v AP grows more quickly as the snowball gets bigger. In this question, you will find the rate of change of the volume- at the instant the radius r is 6 inches. a) First, apply geometry to the situation. Can you think of an equation that relates the variables r and V to each other (assuming the snowball is in the shape of a sphere). b) Now the variables V and r change as time changes, so we can think of them as a function of t. Implicitly differentiate the equation you came up with in part (a) with respect to t. c) What is the rate of change of the radius (read the paragraph above again to find out)? Use this to simplify your equation from part (b). d) What is the rate of change of V when the radius of the snowball is 6 inches?

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.