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#### An Introduction to Geometric Modeling

(10 Questions)Exercise problems related to Big Math 3, First Chapter

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A conical pile of road salt has a diameter of 112 feet and a slant height of 65 feet. The volume of the pile = ---------------.

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Two cans of regular soda and two cans of diet soda are in a container full of water. The two regular cans sink, but the two diet can float. Why?

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Sketch and describe a solid when the region enclosed by y=0, x=0 and y = -x+4 is rotated around the y axis. The volume of the solid formed \approx ------------------- cubic units.

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Imagine a plane slicing through a solid. The intersection of the plane and the solid is called a cross section. Look at the figure and name the shape of the cross section formed.

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A solid of revolution is a three-dimensional figure that is formed by rotating a two-dimensional shape around an axis. The line around which the slope is rotated is called the axis of revolution.In the above figure, there is a rectangle which when is rotated along the axis becomes a three-dimensional solid which is a cylinder with a height of 9 units and a base radius of 4 units. Find the surface area and the volume of this solid. Take the value of \pi = 3.14

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You are using a 9-inch roller to paint. This roller has a diameter of 1\frac{5}{8}inches and a nap of \frac{1}{4}inches as shown.The nap is the fuzzy material on the top of the roller. The area covered by the roller in one revolution is -------------- Take the value of \pi as 3.14.

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Density is the amount of matter that an object has in a given unit of volume and is calculated by the formula density = \frac{mass}{volume}. The height of the tree trunk is 20 meters and base diameter is 0.5 meters. The wood has a density of 380 kilograms per cubic meter. Find the mass of the trunk to the nearest kilogram. Hint: The tree is in the shape of a cylinder, so find the volume and calculate mass using the formula given. Take the value of \pi = 3.14 and round off the answer to the nearest tenth.

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A playground ball with a 16-inch diameter has a rubber coating on its surface. Does a ball with a diameter which is \frac{1}{4} times the diameter of the given ball need \frac{1}{4} times the rubber coating? Hint: the surface area of a ball is the same as that of a sphere which is 4\pi{r}{^2} , so we need to find the surface area of the smaller ball and divide it with the surface area of the bigger ball to get the required answer.

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The figure describes the composite solid that is produced when the solid when the region enclosed by y=0, y= x and x=5 is rotated around the y-axis. Find the volume of this composite solid. Take the value of \pi as 3.14.

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The population density of a city, country or state is a measure of how many people live in a given area. It is usually given in square miles and it can be calculated by using the formula population density = \frac {\text{number of people}}{\text{area of land}} . A circular region with a 4-mile radius has a population density of 6366 people per square mile. Find the number of people who live in that region.

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by Sangeetha Pulapaka