Kerala SSLC · Mathematics · Class 10

Solids: Important Questions with Answers

These are 10 important multiple-choice questions from the Kerala SSLC Mathematics chapter “Solids” (Kerala SCERT syllabus). Each one shows the correct answer and a short explanation of why it is right. Try answering before you read the answer. ExamSummary has 20 practice questions on this chapter in total.

1. Q1.Two solids have the same radius and height. One is a right circular cylinder and the other is a right circular cone. What is the ratio of their volumes?

   • A)1:3
   • B)3:1
   • C)1:1
   • D)2:3

   Answer: B) 3:1

   The volume of a cylinder is πr²h while the volume of a cone is 1/3πr²h. Therefore, the cylinder holds three times the volume of the cone when dimensions are identical.

2. Q2.A toy is made by joining a cone and a hemisphere at their bases. Which surfaces contribute to the total surface area of the toy?

   • A)CSA of cone only
   • B)CSA of cone + CSA of hemisphere
   • C)TSA of cone + TSA of hemisphere
   • D)CSA of cone + TSA of hemisphere

   Answer: B) CSA of cone + CSA of hemisphere

   Since the bases are joined, the circular faces are internal and not part of the external surface area. Only the curved surfaces of both shapes are exposed.

3. Q3.A hollow cylindrical pipe has an outer radius R, inner radius r, and length h. What is the formula for the volume of the material used to make the pipe?

   • A)πR²h
   • B)πr²h
   • C)π(R² - r²)h
   • D)π(R + r)h

   Answer: C) π(R² - r²)h

   The volume of the material is the difference between the volume of the outer cylinder and the inner empty cylinder. This results in the formula π(R² - r²)h.

4. Q4.If the radius of a cylinder is doubled and its height is halved, how does the volume change compared to the original?

   • A)Doubles
   • B)Halves
   • C)Remains the same
   • D)Becomes four times

   Answer: A) Doubles

   The new volume becomes π(2r)²(h/2) = 2πr²h. Comparing this to the original πr²h, the new volume is exactly twice the original.

5. Q5.A canvas tent is shaped like a cylinder surmounted by a cone. If the radius is 5m, cylinder height 4m, and cone slant height 5m, what is the area of canvas required?

   • A)65π m²
   • B)40π m²
   • C)25π m²
   • D)90π m²

   Answer: A) 65π m²

   Canvas area equals the sum of the Curved Surface Area of the cylinder and the cone. Calculating 2πrh + πrl gives 40π + 25π = 65π square meters.

6. Q6.A solid sphere of radius 3 cm is melted and recast into a long cylindrical wire of radius 1 mm. What property remains constant during this process?

   • A)Surface Area
   • B)Density
   • C)Volume
   • D)Shape

   Answer: C) Volume

   During the melting and recasting process, the mass and density remain constant, ensuring that the volume of the material before and after transformation stays the same.

7. Q7.A cylindrical well has a diameter of 14m and a depth of 10m. How much earth was removed to dig it?

   • A)490π m³
   • B)196π m³
   • C)98π m³
   • D)49π m³

   Answer: A) 490π m³

   The volume of earth removed equals the volume of the cylinder formed by the well. With radius 7m and height 10m, the volume is π × 7² × 10 = 490π cubic meters.

8. Q8.A rectangular box contains a single largest possible sphere. If the box is a cube with side 10cm, what is the radius of the sphere?

   • A)5 cm
   • B)10 cm
   • C)2.5 cm
   • D)7.5 cm

   Answer: A) 5 cm

   The largest sphere that fits inside a cube touches all faces, meaning its diameter equals the side length of the cube. Therefore, the radius is half of the side length, which is 5 cm.

9. Q9.In a right circular cone, the relationship between slant height (l), radius (r), and height (h) is given by which Pythagorean theorem variation?

   • A)l² = r² + h²
   • B)h² = l² + r²
   • C)r² = l² + h²
   • D)l = r + h

   Answer: A) l² = r² + h²

   The radius, height, and slant height form a right-angled triangle where the slant height is the hypotenuse. Thus, the square of the slant height equals the sum of the squares of the radius and height.

10. Q10.A solid cube of side 6cm is melted to form small cubes of side 2cm. How many small cubes are formed?

    • A)9
    • B)18
    • C)27
    • D)36

    Answer: C) 27

    The volume of the large cube is divided by the volume of the small cube to find the count. Since volume scales with the cube of the side length, (6/2)³ gives 3³ = 27 cubes.

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