MCQ
Numerical: Mensuration 3D — Sphere & Cone MCQ - Practice Questions with Answers
Solve 15 Numerical: Mensuration 3D — Sphere & Cone questions for RAS/RPSC preparation.
Practice questions
Q1For a cone of radius 7 cm, height 24 cm and slant height 25 cm, and for a sphere of radius 7 cm, match the quantities with their values. Use π = 22/7. 1. Cone curved surface area 2. Cone volume 3. Sphere total surface area
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.
Q2Find the total surface area of a sphere whose radius is 7 cm. Use π = 22/7.
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.
Q3A right circular cone has radius 7 cm and height 9 cm. What is its volume? Use π = 22/7.
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.
Q4A conical tent has a base circumference of 44 m and a slant height of 10 m. If no cloth is used for the base, find the area of cloth required. Use π = 22/7.
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.
Q5Match List I with List II and choose the correct option. Use π = 22/7. List I: 1. Total surface area of a sphere of radius 14 cm; 2. Volume of a cone of radius 14 cm and height 9 cm. List II: a. 1848 cm³; b. 2464 cm².
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.
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More questions
6Match the quantities with their correct values, using π = 22/7. P: volume of a sphere of radius 21 cm; Q: volume of a cone of radius 21 cm and height 12 cm.
7Using π = 22/7, find the volume of a solid sphere whose radius is 21 cm.
8A right circular cone has radius 14 cm and height 48 cm. Using π = 22/7, find its curved surface area.
9A solid sphere of radius 6 cm is melted and recast into identical cones, each with radius 3 cm and height 8 cm. How many complete cones can be made?
10A solid sphere of radius 14 cm is melted and recast into a cone whose radius is 28 cm. Using π = 22/7, find the height of the cone.
11For a right circular cone with radius 7 cm and height 24 cm, which statement is correct? Use π = 22/7.
12The radius of a sphere is 7 cm. Using π = 22/7, find its total surface area.
13For a cone with radius 7 cm and slant height 10 cm, which option gives the correct curved surface area? Use π = 22/7.
14For a cone with radius 7 cm and height 24 cm, which statement about its curved surface area is correct? Use π = 22/7.
15A sphere has radius 21 cm. Using π = 22/7, which of the following statements is incorrect?