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A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm. The surface area of the toy is
- a)36 π cm2
- b)33 π cm2
- c)35 π cm2
- d)24 π cm2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A toy is in the form of a cone mounted on a hemisphere with same radiu...
First, we need to find the radius of the hemisphere and the slant height of the cone.
The diameter of the base of the conical portion is 6cm, so the radius is 3cm.
To find the slant height of the cone, we can use the Pythagorean theorem. The height is 4cm and the radius is 3cm, so:
slant height = √(4^2 + 3^2) = 5cm
Now we can calculate the surface area of the toy. The surface area of the cone is:
πrℓ = π(3)(5) = 15π
The surface area of the hemisphere is:
2πr^2 = 2π(3^2) = 18π
Therefore, the total surface area of the toy is:
15π + 18π = 33π
So the answer is (b) 33π cm2.
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The diameter of the base of the conical portion is 6cm, so the radius is 3cm.
To find the slant height of the cone, we can use the Pythagorean theorem. The height is 4cm and the radius is 3cm, so:
slant height = √(4^2 + 3^2) = 5cm
Now we can calculate the surface area of the toy. The surface area of the cone is:
πrℓ = π(3)(5) = 15π
The surface area of the hemisphere is:
2πr^2 = 2π(3^2) = 18π
Therefore, the total surface area of the toy is:
15π + 18π = 33π
So the answer is (b) 33π cm2.
Most Upvoted Answer
A toy is in the form of a cone mounted on a hemisphere with same radiu...
Let's denote the radius of the hemisphere and the cone as r. Since the diameter of the base of the conical portion is 6 cm, we have:
r = 6/2 = 3 cm
Now, let's find the slant height of the cone. We can use the Pythagorean theorem to find it:
l = √(r^2 + h^2) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 cm
The surface area of the cone is given by the formula:
A_cone = πr * l = π * 3 * 5 = 15π cm^2
The surface area of the hemisphere is given by the formula:
A_hemisphere = 2πr^2 = 2π(3^2) = 2π * 9 = 18π cm^2
The total surface area of the toy is the sum of the surface areas of the cone and the hemisphere:
A_toy = A_cone + A_hemisphere = 15π + 18π = 33π cm^2
So, the surface area of the toy is 33π cm^2, which corresponds to option (b).
r = 6/2 = 3 cm
Now, let's find the slant height of the cone. We can use the Pythagorean theorem to find it:
l = √(r^2 + h^2) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 cm
The surface area of the cone is given by the formula:
A_cone = πr * l = π * 3 * 5 = 15π cm^2
The surface area of the hemisphere is given by the formula:
A_hemisphere = 2πr^2 = 2π(3^2) = 2π * 9 = 18π cm^2
The total surface area of the toy is the sum of the surface areas of the cone and the hemisphere:
A_toy = A_cone + A_hemisphere = 15π + 18π = 33π cm^2
So, the surface area of the toy is 33π cm^2, which corresponds to option (b).
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Community Answer
A toy is in the form of a cone mounted on a hemisphere with same radiu...
B)48
c)72
d)84
First, we need to find the radius of the hemisphere and the slant height of the cone. The radius of the hemisphere is half of the diameter of the base of the cone, which is 3 cm. The slant height of the cone can be found using the Pythagorean theorem:
slant height = √(radius^2 + height^2)
slant height = √(3^2 + 4^2)
slant height = √25
slant height = 5
Now, we can find the surface area of the toy. The surface area of the cone is:
cone surface area = πrℓ
cone surface area = π(3)(5)
cone surface area = 15π
The surface area of the hemisphere is:
hemisphere surface area = 2πr^2
hemisphere surface area = 2π(3^2)
hemisphere surface area = 18π
So, the total surface area of the toy is:
total surface area = cone surface area + hemisphere surface area
total surface area = 15π + 18π
total surface area = 33π
We can use the approximation π ≈ 3.14 to estimate the surface area:
total surface area ≈ 33(3.14)
total surface area ≈ 103.62
So, the surface area of the toy is approximately 103.62 square cm. None of the given answer choices are correct, so the closest answer is 84 (d).
c)72
d)84
First, we need to find the radius of the hemisphere and the slant height of the cone. The radius of the hemisphere is half of the diameter of the base of the cone, which is 3 cm. The slant height of the cone can be found using the Pythagorean theorem:
slant height = √(radius^2 + height^2)
slant height = √(3^2 + 4^2)
slant height = √25
slant height = 5
Now, we can find the surface area of the toy. The surface area of the cone is:
cone surface area = πrℓ
cone surface area = π(3)(5)
cone surface area = 15π
The surface area of the hemisphere is:
hemisphere surface area = 2πr^2
hemisphere surface area = 2π(3^2)
hemisphere surface area = 18π
So, the total surface area of the toy is:
total surface area = cone surface area + hemisphere surface area
total surface area = 15π + 18π
total surface area = 33π
We can use the approximation π ≈ 3.14 to estimate the surface area:
total surface area ≈ 33(3.14)
total surface area ≈ 103.62
So, the surface area of the toy is approximately 103.62 square cm. None of the given answer choices are correct, so the closest answer is 84 (d).
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A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm. The surface area of the toy isa)36 πcm2b)33πcm2c)35πcm2d)24πcm2Correct answer is option 'B'. Can you explain this answer?
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A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm. The surface area of the toy isa)36 πcm2b)33πcm2c)35πcm2d)24πcm2Correct answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm. The surface area of the toy isa)36 πcm2b)33πcm2c)35πcm2d)24πcm2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm. The surface area of the toy isa)36 πcm2b)33πcm2c)35πcm2d)24πcm2Correct answer is option 'B'. Can you explain this answer?.
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