Math Drills
Volume of Composite Solids
C-2Word 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 stone shaped like a cylinder with a radius of 6cm and a height of 15cm was sunk into a rectangular prism water tank that is 50cm deep, 40cm wide, and 15cm in height. What is the volume of the water that overflows from the pond, in how many cm³? Answer □
Answer: 1695.6cm³
(2)A rectangular prism water tank that is 20cm deep, 10cm wide, and 30cm in height had a bar shaped like a cylinder with a radius of 5cm and a height of 30cm sunk into it. What is the volume of the water that overflows from the tank, in how many cm³? Answer □
Answer: 2355cm³
(3)There is a stand shaped by making a square hole that is 6cm deep, 6cm wide, and 10cm in height in a rectangular prism that is 20cm deep, 15cm wide, and 10cm in height. What is the volume of this stand, in how many cm³? Answer □
Answer: 2640cm³
(4)There is a 2-tier cake made of a cylinder with a radius of 6cm and a height of 8cm, topped by a cylinder with a radius of 3cm and a height of 5cm. What is the volume of this cake, in how many cm³? Answer □
Answer: 1045.62cm³
(5)A lump of metal shaped like a rectangular prism that is 10cm deep, 3cm wide, and 3cm in height was sunk into a rectangular prism water tank that is 20cm deep, 15cm wide, and 10cm in height. What is the volume of the water that overflows from the tank, in how many cm³? Answer □
Answer: 90cm³
What to do next
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