\( \begin{array}{l}\text { a } \\ \text { e the } \\ \text { why }\end{array} \left\lvert\, \begin{array}{l}\text { 9. A cone has a volume of } 942 \text { cubic inches } \\ \text { and a height of } 9 \text { inches. What is the radius of } \\ \text { the cone? Use } 3.14 \text { for pi. }\end{array}\right. \)

To find the radius of the cone, we can use the formula for the volume of a cone, which is given by: \[ V = \frac{1}{3} \pi r^2 h \] We know the volume \( V = 942 \) cubic inches and the height \( h = 9 \) inches. Plugging in these values and using \( \pi \approx 3.14 \): \[ 942 = \frac{1}{3} \times 3.14 \times r^2 \times 9 \] Solving for \( r \): 1. Calculate the right side: \[ \frac{1}{3} \times 3.14 \times 9 = 9.42 \] 2. Now set up the equation: \[ 942 = 9.42 r^2 \] 3. Rearranging gives us: \[ r^2 = \frac{942}{9.42} \approx 100 \] 4. Taking the square root of both sides: \[ r \approx 10 \] So, the radius of the cone is approximately \( 10 \) inches! --- In ancient Egypt, pyramids were built with remarkable accuracy, thanks in part to their understanding of geometry. The concept of volume, much like that of a cone, formed the basis of their construction techniques. They even had a special relationship with the number 3.14, which we now use as pi, showing how early civilizations grappled with mathematical concepts long before calculators! In modern industries, understanding shapes and their volumes is crucial! Architects, engineers, and manufacturers need this knowledge to design anything from sleek, space-saving furniture to towering skyscrapers. For example, in designing water tanks shaped like cones, knowing the volume helps determine how much water can be stored. So, whether it’s engineering marvels or everyday objects, this math is ever-present!