Measurement
Spring Release
Open Response and Short Answer Questions
Grade 10 Mathematics MCAS
2010 Spring Release, Mathematics - Grade 10
Question 42: Open-Response
Reporting Category: Measurement
Standard: 10.M.2 - Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area.
Paloma bought a block of wax in the shape of a right rectangular prism. The diagram below shows the block and its dimensions.
a. What is the volume, in cubic centimeters, of the block of wax? Show your work.
Paloma melted the block of wax to make candles. The first candle she made is in the shape of a right circular cylinder. The diagram below represents the candle and its dimensions.
b. What is the volume, in cubic centimeters, of the first candle? Show your work.
c. Paloma wanted to make a second candle in the shape of a right square pyramid with a side length of 10 centimeters and a height of 12 centimeters. Show that she does not have enough remaining wax to make this candle.
d. Paloma decided instead to make the second candle in the shape of a right square pyramid with a side length of 8 centimeters. If she uses all the remaining wax, what will be the height, in centimeters, of the candle? Show your work.
2009 Spring Release, Mathematics - Grade 10
Question 42: Open-Response
Reporting Category: Measurement
Standard: 10.M.1 - Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
Ralph’s company makes doormats. Each doormat is in the shape of a semicircle, as shown in the diagram below.
Each doormat has two parts: a rough fiber interior and a vinyl border.
· The rough fiber interior is in the shape of a semicircle with a diameter of 28 inches.
· The vinyl border has a uniform width of 4 inches. The shaded part in the diagram represents the vinyl border.
a) What is the radius, in inches, of the rough fiber interior? Show or explain how you got your answer.
b) What is the radius, in inches, of the entire doormat? Show or explain how you got your answer.
c) What is the area, in square inches, of the rough fiber interior? Show or explain how you got your answer.
d) What is the area, in square inches, of the vinyl border? Show or explain how you got your answer.
2008 Spring Release, Mathematics - Grade 10
Question 41: Open-Response
Reporting Category: Measurement
Standard: 10.M.2 - Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area.
a. What is the lateral surface area, in square feet, of the tank? Show your work.
b. On the first day of the carnival, the dunking tank was filled with water to a height of 4 feet. What was the volume, in cubic feet, of the water in the tank on the first day of the carnival? Show your work.
At the end of the second day of the carnival, some water was drained from the tank. The volume of water drained was 35.3 cubic feet.c. Using your answer from part (b), determine the height, in feet, of the water remaining in the tank after the water was drained at the end of the second day. Show your work.
The water that was drained from the tank was poured into containers, each in the shape of a right rectangular prism. Each container was 2 feet in length, 1.5 feet in width, and 3 feet in height.d. What was the least number of containers needed to hold all the water that was drained at the end of the second day? Show your work.
2007 Spring Release, Mathematics - Grade 10
Question 41: Open-Response
Reporting Category: Measurement
Standard: 10.M.2 - Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area.
Zachary made a right square pyramid out of plaster for an art project. Each side of his pyramid's base measured 8 inches. The slant height, , of his pyramid measured 5 inches. A diagram of his pyramid is shown below.
a. / What is the area, in square inches, of the base of Zachary's pyramid? Show your work.b. / What is the total surface area, in square inches, of Zachary's pyramid? Show your work.
c. / What is h, the height, in inches, of Zachary's pyramid? Show or explain how you got your answer.
d. / Using the height you determined in part (c), what is the volume, in cubic inches, of Zachary's pyramid? Show your work.
2006 Spring Release, Mathematics - Grade 10
Question 41: Open-Response
Reporting Category: Measurement
Standard: 10.M.1 - Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
The rear window of Alex's van is shaped like a trapezoid with an upper base measuring 36 inches, a lower base measuring 48 inches, and a height of 21 inches. An 18-inch rear window wiper clears a 150° sector of a circle on the rear window, as shown in the diagram below.
a. What is the area, in square inches, of the entire trapezoidal rear window? Show or explain how you got your answer.
b. What fractional part of a complete circle is cleared on the rear window by the 18-inch wiper? Show or explain how you got your answer.
c. What is the area, in square inches, of the part of the rear window that is cleared by the wiper? Show or explain how you got your answer.
d. What percent of the area of the entire rear window is cleared by the wiper? Show or explain how you got your answer.
Short Answer Questions – Measurement
2010 Spring Release, Mathematics - Grade 10
Question 16: Short-Answer
Reporting Category: Measurement
Standard: 10.M.1 - Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
Yoshi is designing a monument that has a triangular base. He drew to represent the base of the monument, as shown in the diagram below.
Based on the measurements in the diagram, what is the area, in square meters, of ?
2010 Spring Release, Mathematics - Grade 10
Question 18: Short-Answer
Reporting Category: Measurement
Standard: 10.M.2 - Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area.
The diagram below shows a right circular cone with a radius of 5 centimeters and a slant height of 10 centimeters.
What is the lateral surface area, in square centimeters, of the cone?
(You may leave your answer in terms of π.)
2009 Spring Release, Mathematics - Grade 10
Question 15: Short-Answer
Reporting Category: Measurement
Standard: 10.M.1 - Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
The diagram below shows parallelogram MNPQ and one of its dimensions.
The perimeter of parallelogram MNPQ is 54 centimeters.
What is the length, in centimeters, of NP ?
2008 Spring Release, Mathematics - Grade 10
Question 16: Short-Answer
Reporting Category: Measurement
Standard: 10.M.1 - Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
Rectangle KLMN and its dimensions are shown below. Point P lies on .
What is the area, in square centimeters, of NPM?
2007 Spring Release, Mathematics - Grade 10
Question 18: Short-Answer
Reporting Category: Measurement
Standard: 10.M.1 - Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
Hannah needs to know the area of the garden in order to buy the correct amount of fertilizer. Based on the dimensions in the diagram, what is the area, in square yards, of Hannah's garden?
2006 Spring Release, Mathematics - Grade 10
Question 18: Short-Answer
Reporting Category: Measurement
Standard: 10.M.2 - Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area.
The volume of Anand's cube is 8 cubic centimeters.
What is the total surface area, in square centimeters, of his cube?