Math Drills
Volume of Composite Solids
C-1Word Problems
What this worksheet covers
Grade 6 (Elementary School) / Volume of Prisms and Cylinders / Volume of Composite Solids
The partners are solids made by stacking two or three basic columns or by hollowing them out. A rectangular prism with a cylindrical hole driven through it, a Prism on Top of a Cylinder, cylinders of different thickness stacked in two tiers, a pipe with its inside taken out and more are found by splitting and adding or by hollowing and subtracting, as calculation, with one word problem opening from a scene added on.
In a pipe with its inside taken out, expressions get set up that take the difference between the outer and inner radii as a radius in itself. To leave out what was removed, the inner radius multiplied by itself is subtracted from the outer radius multiplied by itself. Whether the subtraction sits at the stage of the radii or at the stage after each has been multiplied by itself is what separates them.
Solids handled one at a time have come back here in combination. In Surface Area of Prisms and Cylinders, which waits ahead, the measurements of the same solids are used just as they are while only the quantity being found changes.
- Word Problems5 questions
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Problems and answers on this worksheet
These are the problems in “Volume of Prisms and Cylinders”, shown with their answers.
(1)A metal bar shaped like a cylinder with a radius of 4cm and a height of 20cm was sunk into a rectangular prism water tank that is 40cm deep, 30cm wide, and 20cm in height. What is the volume of the water that overflows, in how many cm³? Answer □
Answer: 1004.8cm³
(2)There is a T-shaped solid. The horizontal part is a rectangular prism that is 30cm deep, 5cm wide, and 8cm in height, and the vertical part is a rectangular prism that is 8cm deep, 5cm wide, and 15cm in height. What is the volume of this solid, in how many cm³? Answer □
Answer: 1800cm³
(3)A lump of metal shaped like a rectangular prism that is 5cm deep, 4cm wide, and 15cm in height was sunk into a rectangular prism water tank that is 30cm deep, 20cm wide, and 25cm in height. What is the volume of the water that overflows from the tank, in how many cm³? Answer □
Answer: 300cm³
(4)There is a water storage tank model shaped with a cylinder tank that has a radius of 8cm and a height of 10cm, topped by a cylinder with a radius of 4cm and a height of 6cm. What is the volume of this model, in how many cm³? Answer □
Answer: 2311.04cm³
(5)On the bottom of a rectangular prism water tank that is 25cm deep, 20cm wide, and 12cm in height, a stand shaped like a cylinder with a radius of 4cm and a height of 12cm is fixed in place. What is the volume of the water that fits into this tank, in how many cm³? Answer □
Answer: 5397.12cm³
What to do next
More worksheets in this unit
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3Volume of Prisms and Cylinders Finding the Volume (Prism ②)
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3Volume of Prisms and Cylinders Word Problems
3Volume of Composite Solids Finding the Volume (Prism − Cylinder and More)
3Volume of Composite Solids Finding the Volume (2-Tier Cylinders and More)