Question 6: A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
Solution: Given, Diameter of the capsule=5mm
Radius of this capsule = `\frac{D}{2}`= 2.5mm
Surface Area of capsule = CSA of Cylinders +2 (CSA of hemisphere)
= 2πrh + 2(2`πr^2)`
= 2πr [h+2r]
[As, (h+2r)= height of Cylinder + 2 x Radius of hemisphere] = Total height of entire capsule = 14mm]
= 2x `\frac{22}{7}` x 2.5 x 14 =` 220 mm^2`
Question Number: 6
Question 7: A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per `m^2`. (Note that the base of the tent will not be covered with canvas.)
Solution: Diameter of the tent = 4m
.: Radius of the tent = `\frac{4}{2}`=2m.
height of the cylinder = 2.1m
Slant height of the come = 2.8m
.: Total Surface Area of tent = CSA of cylinder + CSA of Cone =`2πrh + πrl`
= πr [2h+l] = `\frac{22}{7}` x 2 [ 2x2·1 + 2·8] =44`m^2`
Cost of Canvas for 1` m^2` = 500 rs
Cost of canvas for 44 `m^2` = 500x44 = 22,000 rs
Question Number: 7
Question 8: From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm square.
1st Method
Total S.A of Solid = C.S.A of cylinder + C.SA of Cone+ S. A. of base
= 2πrh+ πrl + `πr^2`
= π r [2h+ l+ r]
Slant height l = `\sqrt{h^2 + r^2}`= `\sqrt{2.4)^2+ (0.7)^2}` = `\sqrt{6.25}` = 2.5
from (1)
T.S.A of Solid = `\frac{22}{7}` x 0.7 [2x2.4 + 2·5 +0.7]= 17.6 `cm^2`
Method II
Total S.A of Solid = T.S.A of cylinder + C.SA of Come - S.A. of Top
=2 πr [h+r] + πrl- π r^2
= πr [ 2h+2r+ l-r] ........(1)
Slant height (l)= `sqrt{h^2 + r^2}` =2.5
from (1)
T.S.A of Solid = `frac{22}{7}` x 0.7 [2x 2.4 +2(0.7) +2.5-0.7]
= 17.6 `cm^2`
Question Number: 8
Method-1
Question Number: 8
Method-2
Question 9: A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
Solution:
Total S.A. of Solid = C.S.A of cylinder+ 2 (C.S.A of hermisphere)
= 2π rh + 2(2`πr^2`)
= 2πr [h+2r]
=2x `\frac{22}{7}` x 3.5 [ 10 + 2(3.5)]
= 374 `cm^2`
Question Number: 9
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