Similar Solids Worksheet - Grade 11 Geometry
Explore the properties of similar solids, including their ratios of corresponding linear measures, areas, and volumes, with these challenging problems.
Includes
Standards
Similar Solids Worksheet
Name:
Date:
Score:
Read each question carefully and answer to the best of your ability. Show all work for full credit.
1. Two similar cylinders have radii in the ratio 2:3. What is the ratio of their surface areas?
2:3
4:9
8:27
16:81
2. If the ratio of the volumes of two similar cones is 64:125, what is the ratio of their corresponding heights?
4:5
8:10
16:25
64:125
3. For similar solids, if the ratio of corresponding linear measures is a:b, then the ratio of their surface areas is , and the ratio of their volumes is .
4. Two spheres are similar. If the diameter of the larger sphere is three times the diameter of the smaller sphere, then the volume of the larger sphere is times the volume of the smaller sphere.
5. A triangular prism has a volume of 100 cm³. A similar triangular prism has a corresponding side length that is twice as long. What is the volume of the larger prism?
6. Two similar rectangular prisms have surface areas of 50 in² and 450 in². If the length of the smaller prism is 5 inches, what is the length of the larger prism?
7. Consider two similar cubes. The smaller cube has a side length of 4 cm.
(a) If the ratio of the side lengths of the smaller cube to the larger cube is 1:2, what is the side length of the larger cube?
(b) Calculate the ratio of their surface areas (smaller to larger).
(c) Calculate the ratio of their volumes (smaller to larger).
8. A cylindrical water tank has a height of 10 feet and a radius of 4 feet. A second similar cylindrical tank has a radius of 6 feet.
(a) What is the ratio of their radii (first tank to second tank)?
(b) Find the height of the second tank.
(c) If the first tank holds 500 cubic feet of water, how much water can the second tank hold (to the nearest whole number)?
9. All cones are similar to each other.
True
False
10. If two solids are similar, their corresponding angles are congruent.
True
False
Related Worksheets
Segment Length Practice Worksheet
Grade 11 Math worksheet focusing on calculating and applying segment lengths in various geometric contexts, including number lines, coordinate planes, and geometric figures.
Similar Figures Worksheet
This worksheet focuses on understanding and applying the properties of similar figures, including triangles and polygons, at a Grade 11 level. Students will solve problems involving scale factors, missing side lengths, and angle measures.
Secants in Circles Worksheet
Explore properties of secant lines in circles, including the Secant-Secant Theorem and tangent-secant relationships, with this Grade 11 mathematics worksheet.
Secant-Tangent Theorem Worksheet
Explore and apply the Secant-Tangent Theorem to solve for unknown lengths and angles in circles.
Triangular Prisms: Surface Area and Volume
This worksheet focuses on calculating the surface area and volume of triangular prisms, suitable for Grade 11 math students.
Triangle Sum Theorem Worksheet
A Grade 11 math worksheet focusing on the Triangle Sum Theorem, including various problem types to reinforce understanding of triangle angle properties.
Eccentricity of Conic Sections
This worksheet focuses on understanding and calculating the eccentricity of conic sections, including ellipses, hyperbolas, and parabolas, for Grade 11 students.
Perpendicular Bisector Worksheet
Grade 11 Geometry worksheet focusing on understanding, constructing, and applying perpendicular bisectors in various geometric contexts.