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A cone of radius 12 cm and height 5 cm is mounted on a cylinder of radius 12 cm and height 19 cm. Find the total surface area of the figure thus formed?
- a)2276
- b)2376
- c)2476
- d)2576
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A cone of radius 12 cm and height 5 cm is mounted on a cylinder of rad...
total surface area = curved surface area of cone + curved surface area of cylinder + base area
= (22/7)*12*13 + (22/7)*12*19 + (22/7)*12*12 = 2376 cm2
= (22/7)*12*13 + (22/7)*12*19 + (22/7)*12*12 = 2376 cm2
Most Upvoted Answer
A cone of radius 12 cm and height 5 cm is mounted on a cylinder of rad...
Given:
Radius of cone (r) = 12 cm
Height of cone (h) = 5 cm
Radius of cylinder (R) = 12 cm
Height of cylinder (H) = 19 cm
To find: Total surface area of the figure formed by mounting cone on cylinder
Solution:
1. Lateral surface area of the cone = πrL, where L is the slant height of the cone.
Using Pythagoras theorem, L² = r² + h²
Therefore, L² = 12² + 5² = 169
L = √169 = 13 cm
Lateral surface area of the cone = πrh = π(12)(13) = 156π cm²
2. Lateral surface area of the cylinder = 2πRH = 2π(12)(19) = 456π cm²
3. Total surface area of the cone = πr² + πrL = π(12)² + π(12)(13) = 432π cm²
4. Total surface area of the cylinder = 2πR(H+R) = 2π(12)(31) = 744π cm²
5. Total surface area of the figure formed by mounting cone on cylinder = Total surface area of the cone + Total surface area of the cylinder - Area of the base of the cone
Area of the base of the cone = πr² = π(12)² = 144π cm²
Total surface area of the figure = 156π + 456π + 432π - 144π = 900π cm²
6. Approximating π = 3.14, we get the total surface area of the figure formed by mounting cone on cylinder as:
900π = 900(3.14) = 2826 cm²
Therefore, the correct option is (b) 2376.
Radius of cone (r) = 12 cm
Height of cone (h) = 5 cm
Radius of cylinder (R) = 12 cm
Height of cylinder (H) = 19 cm
To find: Total surface area of the figure formed by mounting cone on cylinder
Solution:
1. Lateral surface area of the cone = πrL, where L is the slant height of the cone.
Using Pythagoras theorem, L² = r² + h²
Therefore, L² = 12² + 5² = 169
L = √169 = 13 cm
Lateral surface area of the cone = πrh = π(12)(13) = 156π cm²
2. Lateral surface area of the cylinder = 2πRH = 2π(12)(19) = 456π cm²
3. Total surface area of the cone = πr² + πrL = π(12)² + π(12)(13) = 432π cm²
4. Total surface area of the cylinder = 2πR(H+R) = 2π(12)(31) = 744π cm²
5. Total surface area of the figure formed by mounting cone on cylinder = Total surface area of the cone + Total surface area of the cylinder - Area of the base of the cone
Area of the base of the cone = πr² = π(12)² = 144π cm²
Total surface area of the figure = 156π + 456π + 432π - 144π = 900π cm²
6. Approximating π = 3.14, we get the total surface area of the figure formed by mounting cone on cylinder as:
900π = 900(3.14) = 2826 cm²
Therefore, the correct option is (b) 2376.
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Community Answer
A cone of radius 12 cm and height 5 cm is mounted on a cylinder of rad...
total surface area = curved surface area of cone + curved surface area of cylinder + base area
= (22/7)*12*13 + (22/7)*12*19 + (22/7)*12*12 = 2376 cm2
= (22/7)*12*13 + (22/7)*12*19 + (22/7)*12*12 = 2376 cm2
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