Numerical: Mensuration 3D — Sphere & Cone MCQ — 15 Practice Questions with Answers

Explanation

Cone curved surface area = πrl = 22/7 × 7 × 25 = 550 cm². Cone volume = (1/3)πr²h = (1/3) × 22/7 × 7 × 7 × 24 = 1232 cm³. For the sphere of radius 7 cm, total surface area = 4πr² = 4 × 22/7 × 7 × 7 = 616 cm². Checking each quantity in the same order gives the required matching. Thus the correct matching is 1-550 cm², 2-1232 cm³ and 3-616 cm².

Explanation

For a sphere, total surface area = 4πr². Here r = 7 cm and π = 22/7. So, area = 4 × 22/7 × 7² = 4 × 22/7 × 49. Since 49 ÷ 7 = 7, the value becomes 4 × 22 × 7 = 616. Therefore, the total surface area of the sphere is 616 cm². The formula for a sphere has no separate base or height term.

Explanation

The volume of a cone is 1/3 × πr²h. Here r = 7 cm, h = 9 cm and π = 22/7. Volume = 1/3 × 22/7 × 7² × 9 = 1/3 × 22/7 × 49 × 9. Since 49 ÷ 7 = 7 and 9 ÷ 3 = 3, the volume is 22 × 7 × 3 = 462 cm³. Hence, the required volume is 462 cm³.

Explanation

Only the curved surface of the conical tent needs cloth. The base circumference is 44 m, so 2πr = 44. With π = 22/7, 2 × 22/7 × r = 44, giving r = 7 m. Curved surface area of a cone = πrl. Therefore, cloth area = 22/7 × 7 × 10 = 220 m². No base area is added because the question says that no cloth is used for the base.

Explanation

For the sphere, total surface area = 4πr² = 4 × 22/7 × 14². Since 14² = 196 and 196 ÷ 7 = 28, the area is 4 × 22 × 28 = 2464 cm², so 1 matches b. For the cone, volume = 1/3 × πr²h = 1/3 × 22/7 × 14² × 9. This becomes 22 × 28 × 3 = 1848 cm³, so 2 matches a. Hence, 1-b, 2-a is correct.