Composite Volume
A figure is made of a cone (radius 3 cm, height 4 cm) sitting on top of a cylinder (radius 3 cm, height 6 cm). This is the total volume of the figure.
What is 207.24 cm³?
This is the shape of the cross section formed when any flat plane slices through a sphere.
What is a circle?
This is the 3D solid formed when a rectangle is rotated 360° about one of its sides.
What is a cylinder?
A family wants to pay less than $200 per square foot. A 2,400 square foot home is listed at $456,000. This is the cost per square foot.
What is $190 per square foot?
A sphere, a cylinder, and a cone all have the same radius r, and the cylinder and cone both have height equal to 2r. This equation relates the volume of the sphere to the other two.
What is V_sphere = V_cylinder − V_cone?
A hemisphere with radius 6 cm sits on top of a cone with radius 6 cm and height 8 cm. This is the total volume of the figure. (Use π ≈ 3.14)
What is 753.6 cm³?
A plane cuts a cylinder parallel to its base. Then a different plane cuts the same cylinder perpendicular to its base through the center. These are the two cross-sectional shapes produced.
What are a circle and a rectangle?
This is the 3D solid formed when a right triangle is rotated 360° about one of its legs.
What is a cone?
Of the following — textbook, basketball, soup can, filing cabinet, traffic cone — these are the objects best modeled as rectangular prisms.
What are a textbook and a filing cabinet?
Two rectangular prisms have the same volume: Prism A is 5 × 5 × 8 and Prism B is 4 × 5 × 10. This prism requires more wrapping paper.
What is Prism B?
A sphere with diameter 6 inches is carved from a wooden cube with side length 6 inches. This is the approximate volume of the leftover wood. (Use π ≈ 3.14)
What is 102.96 cubic inches?
Of these four shapes — circle, triangle, trapezoid, square — this one is NOT a possible cross section of a cone.
What is a square?
This is the 3D solid formed when a semicircle is rotated 360° about its diameter.
What is a sphere?
Box A (10 in × 8 in × 6 in) costs $8.40. Box B (14 in × 10 in × 5 in) costs $9.80. This box has the lower cost per cubic inch, and this is that cost.
What is Box B at approximately $0.014 per cubic inch?
A cylinder and a cone share the same radius (5 cm) and height (12 cm). This is the difference in their volumes. (Use π ≈ 3.14)
What is 628 cm³?
A closed cylindrical container (diameter 10 cm, height 15 cm) is packed with 6 balls, each with diameter 5 cm. This is the volume of empty space inside the container. (Leave answer in terms of π.)
What is 250π cm³?
A single plane slices through a rectangular prism and intersects exactly three faces. This is the shape of the resulting cross section.
What is a triangle?
A right trapezoid with parallel sides of different lengths is rotated 360° about the side perpendicular to both parallel sides. This is the 3D solid that results.
What is a frustum (truncated cone)? Also acceptable: a cone without a top
A farmer fills a cylindrical grain bin (diameter 18 ft, height 20 ft) with grain that costs $0.50 per cubic foot. This is the approximate total cost. (Use π ≈ 3.14)
What is approximately $2,543.40?
Box A (9 cm × 5 cm × 3 cm) and Box B (7 cm × 6 cm × 3 cm) are gift wrapped with no overlap. This is how many more square centimeters of wrapping paper the larger box needs.
What is 12 cm²? (Box A uses more.)
A grain silo is a cylinder (radius 4 m, height 10 m) topped with a hemisphere (radius 4 m). A cone-shaped pile of grain (radius 4 m, height 3 m) sits on the floor inside. This is the volume of air space remaining. (Leave answer in terms of π.)
What is 560π/3 m³?
A single plane slices through a cube and passes through exactly one point on each of the cube's 6 edges (one per face). This is the shape of the resulting cross section.
What is a regular hexagon?
A 6 cm × 10 cm rectangle is rotated 360° about the line connecting the midpoints of the two 10-cm sides. This is the resulting solid and its volume. Leave your answer in terms of π.
What is a cylinder with volume 150π cm³?
A concrete slab is 10 ft × 12 ft × 6 inches deep. Around the inside perimeter is a footing trench that is 1 ft wide and an additional 8 inches deeper than the slab. This is the total volume of concrete needed, in cubic feet.
What is approximately 86⅔ ft³ (or 260/3 ft³)?
A sphere is inscribed inside a cylinder so that the sphere touches the top, bottom, and side of the cylinder. This is the ratio of the sphere's volume to the cylinder's volume, expressed as a fraction.
What is 2/3?