Exam 10: Modeling With Geometry

Solve the problem. -The water reservoir for a city is shaped like a rectangular prism 295 meters long, 108 meters wide, and 18 meters deep at the end of the day, the reservoir is 90% full. How much water must be Added overnight to fill the reservoir?

Solve. Round your answer to the nearest tenth. -Find the circumference of a circle with a diameter of 13 feet.

Provide an appropriate response. -In fractal geometry, the perimeter of a region is and the area is .

Solve. Round your answer to the nearest tenth. -Find the area of a circle with a diameter of 38 feet.

Find the perimeter. -

Refer to the given map. Assume that the length of each east-west block is $\frac { 1 } { 8 }$ mile and the length of each north-southblock is $\frac { 1 } { 4 }$ mile. -Find the shortest possible walking distance (following the streets)between the bus stop and the grocery store.

Provide an appropriate response. -In a right triangle, the square of the length of the hypotenuse is equal to the ________.

Provide an appropriate response. -Solving for fractal dimension, we use the rule that .

Provide an appropriate response. -To create a Sierpinski triangle, start with a solid black triangle and iterate what rules?

Solve the problem. -A semi-circular transom above a door is to contain a stained glass window. If the stained glass window costs $1.40 per square inch, how much will the window cost?

Refer to the given map. Assume that the length of each east-west block is $\frac { 1 } { 8 }$ mile and the length of each north-southblock is $\frac { 1 } { 4 }$ mile. -Find the straight-line distance between the bus stop and the grocery store.

Refer to the given map. Assume that the length of each east-west block is $\frac { 1 } { 8 }$ mile and the length of each north-southblock is $\frac { 1 } { 4 }$ mile. -Find the shortest possible walking distance (following the streets)between the grocery store and the library.

Solve the problem. -Steve is 8% taller than Andy but proportioned in exactly the same way. If Andy is 217 pounds, how much does Steve weigh?

Solve the problem. -If you magically doubled in size, by what factor has your arm length increased?

Refer to the given map. Assume that the length of each east-west block is $\frac { 1 } { 8 }$ mile and the length of each north-southblock is $\frac { 1 } { 4 }$ mile. -Find the shortest possible walking distance (following the streets)between the bus stop and the library.

Solve the problem. -Suppose you build an architectural model of a new concert hall using a scale factor of 22. How will the height of the actual concert hall compare to the height of the scale model.

Solve the problem. -Steve is 21% taller than Andy but proportioned in exactly the same way. If Andy's waist is 44 inches, what is Steve's waist?

Solve the problem. -Suppose you build an architectural model of a new concert hall using a scale factor of 39. How will the surface area of the actual concert hall compare to the surface area of the scale model?

Solve the problem. -A driveway is shaped like a parallelogram. How much asphalt (in square yards)is needed to pave the driveway?

Provide an appropriate response. -Two triangles are similar if they have the same size, but not necessarily the same shape.