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प्रश्न
The circumferences of circular faces of a frustum are 132 cm and 88 cm and its height is 24 cm. To find the curved surface area of the frustum complete the following activity.( \[\pi = \frac{22}{7}\])
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उत्तर
(Circumference)1 = 2πr1 = 132
∴ r1 = `132/(2π) = (132 xx 7)/(2 xx 22)` = 21 cm
(Circumference)1 = 2πr2 = 88
r2 = `88/(2π) = (88 xx 7)/(2 xx 22)`
= 14 cm
Slant height of frustum, `l = sqrt(h^2 + (r_1 - r_2)^2`
= `sqrt((24)^2 + (21 - 14)^2`
= `sqrt((24)^2 + (7)^2`
= `sqrt(576 + 49)` = `sqrt(625)`
= `sqrt(25 xx 25)` = 25 cm
Curved surface area of the frustum = `π(r_1 + r_2)l`
= `22/7 (21 + 14) xx 25`
= `22/7 xx 35 xx 25`
= 2750 cm2
संबंधित प्रश्न
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- the volume of water which can completely fill the bucket;
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The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm, respectively. Find the slant height of the frustum.
Choose the correct answer of the following question:
If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm, then its slant height is
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A drinking glass is in the shape of the frustum of a cone of height 21 cm with 6 cm and 4 cm as the diameters of its two circular ends. Find the capacity of the glass.
A frustum of a right circular cone is of height 16 cm with radius of its ends as 8 cm and 20 cm. Then, the volume of the frustum is
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The radii of the top and bottom of a bucket of slant height 13 cm are 9 cm and 4 cm respectively. The height of the bucket is ______.
Find the total surface area of frustum, if its radii are 15 cm and 7 cm. Also, the slant height of the frustum is 14 cm.
Radii of the frustum = `square` cm and `square` cm
Slant height of the frustum = `square` cm
Total surface area = `π[(r_1^2 + r_2^2 + (r_1 + r_2)l]`
= `22/7 [square + square + (square + square) square]`
= `22/7 (square)`
= `square` cm2
Hence, the total surface area of the frustum is `square`.
