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. - Mathematics

Advertisements
Advertisements

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.

`["Assume "pi=22/7]`

 

Advertisements

Solution

(i) Let ABC be a conical tent.

Height (h) of conical tent = 10 m

Radius (r) of conical tent = 24 m

Let the slant height of the tent be l.

In ΔABO,

AB2 = AO2 + BO2

l2 = h2 + r2

= (10 m)2 + (24 m)2

= 676 m2

∴ l = 26 m

Therefore, the slant height of the tent is 26 m.

 

(ii) CSA of tent = πrl

`=(22/7xx24xx26)m^2`

`=13728/7m^2`

Cost of 1 m2 canvas = Rs 70

`"Cost of "13728/7m^2" canvas "=Rs.(13728/7xx70)`

= Rs. 137280

Therefore, the cost of the canvas required to make such a tent is Rs 137280.

  Is there an error in this question or solution?
Chapter 13: Surface Area and Volumes - Exercise 13.3 [Page 221]

APPEARS IN

NCERT Mathematics Class 9
Chapter 13 Surface Area and Volumes
Exercise 13.3 | Q 4 | Page 221

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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

`["Assume "pi=22/7]`

 


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 "sqrt1.04= 1.02)`

 


The following figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. This common radius is 7 cm. The height of the cylinder and cone are each of 4 cm. Find the volume of the solid.


A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone.


Find the curved surface area of a cone with base radius 5.25 cm and slant height 10cm. 


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

 


The radius and slant height of a cone are In the ratio of 4 : 7. If its curved surface area is 792 cm2, find its radius. (Use it 𝜋 = 22/7).


There are two cones. The curved surface area of one is twice that of the other. The slant height of the later is twice that of the former. Find the ratio of their radii.  


A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius of each is to the height of each as 3:4.


A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3:1. 

 


If the radius of the base of a cone is halved, keeping the height same, what is the ratio of the volume of the reduced cone to that of the original cone?  


Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14 cm.  

 


Find the volume of a cone whose slant height is 17 cm and radius of base is 8 cm. 


The curved surface area of a cone is 12320 cm2. If the radius of its base is 56 cm, find its height. 


The circumference of the base of a 12 m high conical tent is 66 m. Find the volume of the air contained in it. 

 


The radius and the height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the radius and height of the cone (Take π = 3.14) 


A solid sphere and a solid hemi-sphere have the same total surface area. Find the ratio between  their volumes.


A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into a inverted cone of radius 4.8 cm. Find the height of the cone is it is completely filled.


A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5cm. Find the number of sphere formed.


A vessel is in the form of an inverted cone its height is 8 cm and the radius of its top, which is open, is 5 cm. If is filled with water up to the rim. When lead shots each of which is a sphere of radius 0.5 cm are dropped into the vessel, one fourth of the water flows out. Find the number of lead shots sopped in the vessel.


In the following diagram a rectangular platform with a semi-circular end on one side is 22 metres long from one end to the other end. If the length of the half circumference is 11 metres. Find the cost of constructing the platform, 1.5 metres high at the rate of Rs. 4 per cubic metres. 


A solid, consisting of a right circular cone standing one a hemisphere, is placed upright in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of
the hemisphere is 2 cm and the height of cone is 4 cm. Give your answer to the nearest cubic centimeter.


Perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone.


Curved surface area of a cone is 251.2 cm2 and radius of its base is 8 cm. Find its slant height and perpendicular height. (π = 3.14)


What will be the cost of making a closed cone of tin sheet having radius of base 6 m and slant height 8 m if the rate of making is Rs.10 per sq.m? `(π = 22/7)`


volume of a cone is 6280 cubic cm and base radius of the cone is 20 cm. Find its perpendicular height. (π = 3.14)


Surface area of a cone is 188.4 sq.cm and its slant height is 10 cm. Find its perpendicular height ( π= 3.14)


Volume of a cone is 1232 cm3 and its height is 24 cm. Find the surface area of the cone. `( π = 22/7)`


The curved surface area of a cone is 2200 sq.cm and its slant height is 50 cm. Find the total surface area of cone. `(π = 22/7)`


If the ratio of radius of base and height of a cone is 5:12 and its volume is 314 cubic metre. Find its perpendicular height and slant height. (π = 3.14)


Total surface area of a cone is 616 sq.cm. If the slant height of the cone is three times the radius of its base, find its slant height.


Find the radius of the circular base of the cone , if its volume is 154 cm3 and the perpendicular height is 12 cm


The heights of two cones are in the ratio 1:3 and their base radii are in the ratio 3:1. Find the ratio of their volumes. 


The radius and height of a cylinder, a cone and a sphere are same. Calculate the ratio of their volumes. 


The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the: height of the tent.


The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find: external curved surface area .


The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find: total surface area.


The ratio of the base area and the curved surface of a conical tent is 40: 41. If the height is 18 m, Find the air capacity of the tent in terms of n.


A metallic cylinder has a radius of 3 cm and a height of 5 cm. It is made of metal A. To reduce its weight, a conical hole is drilled in the cylinder, as shown and it is completely filled with a lighter metal B. The conical hole has a radius of `3/2` cm and its depth is `8/9` cm. Calculate the ratio of the volume of the metal A to the volume of metal B in the solid.


A right-angled triangle PQR where ∠Q = 90° is rotated about QR and PQ. If QR = 16 cm and PR = 20 cm, compare the curved surface areas of the right circular cones so formed by the triangle


The ratio of the radii of two right circular cones of the same height is 1 : 3. Find the ratio of their curved surface area when the height cone is 3 times the radius of the smaller cone.


The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is


Share
Notifications



      Forgot password?
Use app×