"If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at which the diameter decreases when the diameter is 12 cm."
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.
"If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at which the diameter decreases when the diameter is 12 cm."
I started off with the surface area formula for a sphere, A = 4pi*r^2. I plugged in the diameter divided by 2 for r, radius, in the formula, since we are solving the rate of change of the melting diameter of the snowball with time. This simplifies to A= 4pi*(d^2/4) = pi*d^2. I took the derivative of this to get A'= pi2d(dd/dt). The given dA/dt was -3, so I plugged that into A' and solved for dd/dt, getting -3pi/24, which was incorrect, even when I took off the negative sign, or made it into decimal. Where am I messing something up here? Thanks
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