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A tent is in the form of a cylinder of diameter 8 m and height 2 m, surmounted by a cone of equal base and height 3 m. The canvas used for making the tent is equal to
- a)36 πm2
- b)28 πm2
- c)24 πm2
- d)32 πm2
Correct answer is option 'A'. Can you explain this answer?
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The canvas used for making the tent includes the lateral surface area of the cylinder and the cone, as well as the area of the circular base of the cone.
The lateral surface area of the cylinder is given by:
L = 2πrh
where r is the radius (half the diameter) of the cylinder and h is the height of the cylinder. Substituting r = 4 m and h = 2 m, we get:
Lc = 2π(4)(2) = 16π
The lateral surface area of the cone is given by:
L = πrs
where r is the radius of the base of the cone and s is the slant height (the distance from the vertex of the cone to a point on the edge of the base). Since the cone has equal base and height, its radius is also 4 m. To find the slant height, we can use the Pythagorean theorem:
s^2 = r^2 + h^2
s^2 = 4^2 + 3^2
s^2 = 16 + 9
s^2 = 25
s = 5
Substituting r = 4 m and s = 5 m, we get:
Lc = π(4)(5) = 20π
Finally, the area of the circular base of the cone is:
Ac = πr^2 = π(4)^2 = 16π
Therefore, the total canvas used is:
Ac + Lc + Lc = 16π + 16π + 20π = 52π
This is approximately equal to 163.36 square meters, or 163.4 square meters rounded to one decimal place. So the answer is (d) 163.4.
The lateral surface area of the cylinder is given by:
L = 2πrh
where r is the radius (half the diameter) of the cylinder and h is the height of the cylinder. Substituting r = 4 m and h = 2 m, we get:
Lc = 2π(4)(2) = 16π
The lateral surface area of the cone is given by:
L = πrs
where r is the radius of the base of the cone and s is the slant height (the distance from the vertex of the cone to a point on the edge of the base). Since the cone has equal base and height, its radius is also 4 m. To find the slant height, we can use the Pythagorean theorem:
s^2 = r^2 + h^2
s^2 = 4^2 + 3^2
s^2 = 16 + 9
s^2 = 25
s = 5
Substituting r = 4 m and s = 5 m, we get:
Lc = π(4)(5) = 20π
Finally, the area of the circular base of the cone is:
Ac = πr^2 = π(4)^2 = 16π
Therefore, the total canvas used is:
Ac + Lc + Lc = 16π + 16π + 20π = 52π
This is approximately equal to 163.36 square meters, or 163.4 square meters rounded to one decimal place. So the answer is (d) 163.4.
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A tent is in the form of a cylinder of diameter 8 m and height 2 m, surmounted by a cone of equal base and height 3 m. The canvas used for making the tent is equal toa)36 πm2b)28πm2c)24πm2d)32πm2Correct answer is option 'A'. Can you explain this answer?
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