UPSKILL MATH PLUS

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Methodical recommendation:

Theory

Number Name Description
1. Volume of sphere and hollow sphere Learn how to find out the volume of a sphere and hollow sphere.
2. Volume of hemisphere Learn how to find out the volume of a hemisphere.
3. Frustum of a cone Get introduced to the shape frustum of a cone.

Textbook Questions

Number Name Type Difficulty Marks Description
1. Multiple choice question I Other easy 1 m. Work on the problem to find the answers using volume of sphere, hemisphere and frustum.
2. Multiple choice question II Other easy 1 m. Work on the problem to find the answers using volume of sphere, hemisphere and frustum.
3. Multiple choice question III Other easy 1 m. Work on the problem to find the answers using volume of sphere, hemisphere and frustum.
4. Multiple choice question IV Other easy 4 m. Work on the problem to find the answers using volume of sphere, hemisphere and frustum.
5. Two mark example problem Other medium 2 m. Work on the problem to find the answers using volume of sphere, hemisphere and frustum.
6. Two mark exericse problem Other medium 2 m. Work on the problem to find the answers using volume of sphere, hemisphere and frustum.
7. Five mark example problem I Other hard 5 m. Work on the problem to find the diameter of the second hemisphere using volume of first hemisphere.
8. Five mark example problem II Other hard 5 m. Work on the problem to find the diameter of the second hemisphere using volume of first hemisphere.
9. Five mark exercise problem I Other hard 5 m. Analyse the questions and answer using volume of sphere, hemisphere and frustum.
10. Five mark exercise problem II Other hard 5 m. Analyse the questions and answer using volume of sphere, hemisphere and frustum.
11. Five mark exercise problem III Other hard 5 m. Analyse the questions and answer using volume of sphere, hemisphere and frustum.
12. Five mark exercise problem IV Other hard 5 m. Analyse the questions and answer using volume of sphere, hemisphere and frustum.
13. Five mark exercise problem V Other hard 5 m. Analyse the questions and answer using volume of sphere, hemisphere and frustum.

Practice Questions

Number Name Type Difficulty Marks Description
1. Determine the volume of a sphere Other easy 3 m. Determine the volume of a sphere using radius of the sphere.
2. Find the volume of a hemisphere Other easy 3 m. Practice problem to find the volume of a hemisphere.
3. Find the weight of the box Other easy 3 m. Find the weight of the box using the weight of the Christmas balls.
4. Find the volume of the silver used to make the bowl Other medium 4 m. Work on the problem to find the volume of the silver used to make the bowl using inner radius and thickness of the bowl.
5. Find the volume of the lamp Other medium 4 m. Work on the problem to find the volume of the lamp using surface area.
6. Calculate the volume of a hemisphere Other medium 4 m. Calculate the volume of a hemisphere using the total surface area of a hemisphere.
7. Find the ratio of volumes of two sphere Other medium 4 m. Work on the problem to find the ratio of volume of two spheres using the ratio of radii.
8. How many balls can be made Other medium 4 m. Find the number of smaller balls can be made from the bigger ball.
9. Find the radius of the wood apple Other medium 4 m. Work on the problem to find the radius of the wood apple using the weight of the apple.
10. Find the volume of the frustum Other medium 4 m. Practice problem to find the volume of the frustum.
11. Find the thickness of the bowl Other medium 4 m. Work on the problem to find the thickness of the hemispherical bowl.
12. Find the height of the kulfi Other medium 4 m. Practice problem to find the area of the kulfi using frustum of a cone formula.
13. Find the volume of the material required to make the shell Other medium 4 m. Analyse the question and answer using the given information.
14. Find the time taken to empty the tank Other hard 5 m. Find the time taken to emptry the tank using the formula of volume of hemisphere.
15. Select the correct answers Other hard 4 m. Select the correct answers using the given information.
16. Find the diameter of the second hemisphere Other hard 5 m. Work on the problem to find the diameter of the second hemisphere using volume of first hemisphere.
17. Find the diameter and surface area Other hard 5 m. Find the diameter and surface area of the sphere using volume of the sphere.
18. Find the radius of the lower side of the bucket Other hard 5 m. Work on the problem to find the radius of the lower side of the bucket.
19. Case study: Frustum of a cone Other hard 5 m. Understand the given situation and answer the questions.
20. Calculate the weight of a hollow brass sphere Other hard 5 m. Practice problem to find the volume of the hollow hemisphere.

Key Questions for School Exam Preparation

Number Name Type Difficulty Marks Description
1. Calculate the volume of the frustum Other medium 2 m. Work on the problem to find the answers using volume of sphere, hemisphere and frustum.
2. Calculate the weight of a hollow brass sphere Other hard 5 m. Work on the problem to find the diameter of the second hemisphere using volume of first hemisphere.
3. Prove the following Other hard 5 m. Analyse the question and answer using the given information.
4. Calculate the cost of milk which fills the container Other hard 5 m. Try to find the correct answer using frustum of a cone formula.

Questions for Teacher Use

Number Name Type Difficulty Marks Description
1. Calculate the volume of the iron ball Other easy 3 m. Work on the problem to find the volume of the spherical ball using diameter of the ball.
2. Find the ratio between the volume of sphere and hemisphere Other medium 5 m. Find the ratio between the volume of sphere and hemisphere using surface area.
3. Ratio between the volume of earth and moon Other medium 5 m. Determine the ratio between the volume of earth and moon using the given information.
4. Find the diameter of the bowl Other medium 4 m. Work on the problem to find the diameter of the hemispherical bowl using the volume of the bowl.
5. Select the correct answers Other hard 5 m. Choose the correct answers using surface area of the hemisphere.
6. Find the percentage change in radius Other hard 5 m. Work on the problem to find the percentage change in radius of the sphere.
7. Choose the correct answer Other hard 6 m. Try to find the correct answer using frustum of a cone formula.
8. Find the area and the capacity of the metal bucket Other hard 6 m. Work on the problem to find the area and the capacity of the metal bucket.
9. Ratio of the sphere volumes Other medium 1 m. Work on the problem to find the answers using volume of sphere, hemisphere and frustum.
10. The volume of the frustum of a cone Other medium 1 m. Work on the problem to find the answers using volume of sphere, hemisphere and frustum.
11. Find the volume of a hemisphere Other easy 1 m. Practice problem to find the volume of a hemisphere.

Periodic assessments

Number Name Recomended time: Difficulty Marks Description
1. Homework I 00:20:00 medium 8 m.
2. Homework II 00:20:00 medium 9 m.
3. Homework III 00:20:00 medium 14 m.
4. Homework IV 00:20:00 medium 15 m.
5. Homework V 00:25:00 medium 13 m.
6. Homework VI 00:25:00 medium 16 m.
7. Revision test I 00:20:00 medium 16 m.
8. Revision test II 00:20:00 medium 18 m.
9. Revision test III 00:20:00 medium 20 m.
10. Revision test IV 00:25:00 medium 17 m.
11. Revision test V 00:30:00 medium 18 m.
12. Revision test VI 00:30:00 medium 14 m.
13. Revision test VII 00:30:00 medium 17 m.
14. Periodic Assessment 00:15:00 medium 2 m. PAT 2
15. Periodic Assessment - Extended version 00:10:00 medium 2 m. PA 2
16. Periodic Assessment - 3 00:10:00 medium 2 m. PA3