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Class 9 Maths NCERT Solution for surface area and volume part 3




In this page we have NCERT book Solutions for Class 9th Maths:Surface area and volume for EXERCISE 3 . Hope you like them and do not forget to like , social share and comment at the end of the page.

 

Question 1)

Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.

Question 2)

 Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m?

Question 3)

 Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find radius of the base  And total surface area of the cone. 

Question 4)

A conical tent is 10 m high and the radius of its base is 24 m. Find

(i) Slant height of the tent

(ii) Cost of the canvas required to make the tent, if the cost of 1 m2 canvas is Rs 70. 

Question 5)

What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. [Use π = 3.14]

Question 6)

 The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs 210 per 100 m2

Question 7)

 A joker’s cap is in the form of right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. 

Question 8)

 A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per m2, what will be the cost of painting all these cones? (Use π = 3.14 and take √1.04 =  1.02)..

We are assuming the value of π=22/7 in all the solutions

 

Solution 1:

Diameter of the base of a cone =d=10.5 cm

Radius of the base of a cone =r=5.25 cm

Slant height of the cone =l=10 cm

 Curved Surface Area of the cone =π.r.l= (22/7)×5.25×10=165 cm2

Solution 2

Radius (r) of the base of cone = 12 m

Slant height (l) of cone = 21 m

Total surface area of cone = πr(r + l) =1244.57  m2-

Solution 3:

CSA =308 cm2

Slant height =14cm

Radius of the cone =?

Now CSA =πrl

308=(22/7)X14Xr

R=7 cm

Total surface area

=πrl+πr2

=462 cm2

Solution 4      

Height of the conical tent =h=10 m

Radius of the base of conical tent =r=24 m

Slant height of the conical tent = l = 

Curved Surface Area of the tent =π.r.l=(22/7)×24×26  m2

Cost of canvas to make the tent @Rs 70 per 1 m2

=70×(22/7)×24×26= Rs 137280

Solution 6:

Slant height (l) of conical tomb = 25 m

Base radius (r) of tomb =  7 m

CSA of conical tomb = πrl

= 550 m2

Cost of white-washing 100 m2 area = Rs 210

Cost of white-washing 550 m2- area =Rs (210/100) X550

= Rs 1155

Therefore, it will cost Rs 1155 while white-washing such a conical tomb.

Solution 7:

Base radius of conical cap =r=7 cm

 Height of conical cap =h=24 cm

Slant height of conical cap = l = l = 

Curved Surface area of 1 cap = Area of the sheet required to make 1 cap =π.r.l

=(22/7)×7×25=550 cm2

Solution 8:

Radius of the cone =r=40/2 cm=.2 m

Height of the cone =h=1 m

Slant height of cone = l = l = 

Curved surface of cone=πrl=.64056 m2

Curved surface area of 50cone=50X .64056 m2

Now cost of painting 1m2 =R12

Then cost of painting 50 cone will be =

=12X50X .64056

=Rs 384.556

 

 

 

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