Page 15.62
Type 1
In a right circular cone :
(i) h=4 m and r=3 m , l= __
(ii) l=10 cm and r=7 cm , curved surface area A = _
(iii) r=7 m and h=9m , volume V=__
(iv) l=25 cm and r=7 m , height h=__
(v) l=13 cm and h=12 cm , radius r =__
Sol :
Which of the following will be the relation between their volumes ?
(a) Volume of the cone < Volume of the cylinder
(b) Volume of the cone > Volume of the cylinder
(c) Volume of the cone = Volume of the cylinder
(d) none of these
Sol :
(a) 1:3
(b) 3:1
(c) 4:3
(d) 3:3
Sol :
(a) 3:π
(b) π:3
(c) 1:3
(d) 3:1
Sol :
(a) 2:1
(b) 1:2
(c) 1:4
(d) 4:1
Sol :
(a) 2:1
(b) 1:2
(c) 6:1
(d) 8:1
Sol :
(a) 1:2
(b) 2:1
(c) 1:4
(d) 4:1
Sol :
(a) $\dfrac{32}{75}\pi x^3$
(b) $\dfrac{8}{25}\pi x^3$
(c) $\dfrac{8}{75}\pi x^3$
(d) $\dfrac{2}{25}\pi x^3$
Sol :
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Sol :
(a) 8:1
(b) 2:1
(c) 1:8
(d) 1:4
Sol :
(i) volume
(ii) curved surface area
(iii) total surface area of the cone $\left(\pi =\dfrac{22}7{}\right)$
Sol :
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Sol :
(ii) Find the volume of the greatest right circular cone which can be made out of cutting a cube whose each edge is 28cm
Sol :
Sol :
PAGE 15.65
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TYPE 2
(ii) If height of a cone is 84cm and base radius is 35cm , find the surface area and volume of the cone
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EXERCISE 15.3
Type 1
QUESTION 1
Fill in the blanks :In a right circular cone :
(i) h=4 m and r=3 m , l= __
(ii) l=10 cm and r=7 cm , curved surface area A = _
(iii) r=7 m and h=9m , volume V=__
(iv) l=25 cm and r=7 m , height h=__
(v) l=13 cm and h=12 cm , radius r =__
QUESTION 2
Total surface area of a right circular cone is obtained by S =__Sol :
QUESTION 3
If base and height of a right circular cone and a right circular cylinder be the same :Which of the following will be the relation between their volumes ?
(a) Volume of the cone < Volume of the cylinder
(b) Volume of the cone > Volume of the cylinder
(c) Volume of the cone = Volume of the cylinder
(d) none of these
Sol :
QUESTION 4
Ratio of the volumes of a right circular cylinder and right circular cone is :(a) 1:3
(b) 3:1
(c) 4:3
(d) 3:3
Sol :
QUESTION 5
Which of the following will be the relation between the volume of a cube with edge a cm and a cone having base radius a cm and height a cm :(a) 3:π
(b) π:3
(c) 1:3
(d) 3:1
Sol :
QUESTION 6
Two cones have the same height and ratio of the radii as 1:2 . Which of the following will be the ratio between their volumes ?(a) 2:1
(b) 1:2
(c) 1:4
(d) 4:1
Sol :
QUESTION 7
If radius and height, both of a right circular cone be doubled, which of the following will be the ratio between the volumes of new solid and original solid?(a) 2:1
(b) 1:2
(c) 6:1
(d) 8:1
Sol :
QUESTION 8
If base radius of right circular cone be halved , keeping the height unchanged which of the following will be the ratio between the volumes of original cone and the miniature cone ?(a) 1:2
(b) 2:1
(c) 1:4
(d) 4:1
Sol :
QUESTION 9
The height of a right circular cone is $\dfrac{1}{2}x$ and its base radius is $\dfrac{4}{5}x$ . What will be the volume of the cone ?(a) $\dfrac{32}{75}\pi x^3$
(b) $\dfrac{8}{25}\pi x^3$
(c) $\dfrac{8}{75}\pi x^3$
(d) $\dfrac{2}{25}\pi x^3$
Sol :
QUESTION 10
The radius of the base of a cone is 3cm and height is 7cm , then find its volume .Sol :
QUESTION 11
The radius of the base of a cone is 3cm and height is 4cm , find its volumeSol :
QUESTION 12
The diameter of the base of a conical canvas tent is 14m and its slant height is 6m , find the area of the canvas used in the tent .Sol :
QUESTION 13
Diameters of two cones are same . If their slant heights are in the ratio 5:4 , find the ratio of their curved surfacesSol :
QUESTION 14
There are two cones. The curved surface area of one is twice the curved surface area of the other . The slant height of the second is twice that of the first . Find ratio of their radiiSol :
QUESTION 15
Find the curved surface area of a right circular cone whose slant height is 10cm and base radius is 7cmSol :
QUESTION 16
The height of a cone is 16cm and radius of the base is 12cm . Find the curved surface area of this cone . (Use π=3.14)Sol :
QUESTION 17
The radius of the base of a cone is 7cm and its height is 24cm . Find its total surface area.Sol :
QUESTION 18
The circumference of the base of a 10m high conical tent is 44m . One another conical tent has 20m and circumference 22m . What will be the ratio of the volume of the first and the second tent ?(a) 8:1
(b) 2:1
(c) 1:8
(d) 1:4
Sol :
QUESTION 19
Radius of the base of a cone and height are respectively 35cm and 72cm . Find the(i) volume
(ii) curved surface area
(iii) total surface area of the cone $\left(\pi =\dfrac{22}7{}\right)$
Sol :
QUESTION 20
A conical cup is formed by bending a semicircular metal sheet of diameter 28cm . Find the capacity of the cup.Sol :
QUESTION 21
Curved surface area of a cone is 4970 cm2 and its diameter is 70cm . Find its slant height $\left(\pi =\dfrac{22}{7}\right)$Sol :
QUESTION 22
The slant height of a cone is 7 m and its curved surface area is 440 m2 . Find the radius of its base .Sol :
QUESTION 23
The curved surface area of a right circular cone with radius 11.3 cm is 355 cm2. What is the slant height of the cone ? $\left(\pi=\dfrac{355}{113}\right)$Sol :
QUESTION 24
Total surface area of a cone is 22 m2 . Its slant height is 6 times the radius of the baseSol :
QUESTION 25
The volume of a cone is 770 m3 and its height is 15m . Find the radius of the baseSol :
QUESTION 26
(i) A right triangle with sides 7cm and 12cm forming a right angle is revolved about the 12cm side . Find the volume of the cone so obtained.(ii) Find the volume of the greatest right circular cone which can be made out of cutting a cube whose each edge is 28cm
Sol :
QUESTION 27
First persons live in a conical tent and for each person , 16m2 space on the base and 100m3 air is required . Find the height of the tentSol :
PAGE 15.65
QUESTION 28
A rent of a Circus is cylindrical to a height of 4m and then after height , it is conical above . If its diameter is 112m and slant height of the cone is 75m, find the required total area of the canvasSol :
QUESTION 29
A conical hole of height 8cm and base radius 6 cm is cut out from a solid cylinder of height 8cm and base radius 6cm . Find the volume of the remaining solid.Sol :
QUESTION 30
A tent in the shape of a cone is to be made of canvas. Its diameter of the base is 16m and height is 15m . If width of the canvas is 2.2m , what length in metres of canvas will be required ?Sol :
TYPE 2
QUESTION 31
(i) Find the curved surface area of a right circular cone of height 12 cm with diameter of base as 10cm(ii) If height of a cone is 84cm and base radius is 35cm , find the surface area and volume of the cone
Sol :
QUESTION 32
The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface .Sol :
QUESTION 33
The radius of the base of a right circular cone is 10 cm and its slant height is 15cm . Find the volume and total surface area of the cone.Sol :
QUESTION 34
If area of the curved surface of the cone is 396 m2 and area of its base is 36π m2 , find the slant height of the coneSol :
QUESTION 35
How many opened bags of wheat can be accommodated in a conical tent having radius 8.4m and vertical height 2.5m , if a bag of wheat requires 1.96m3 of space (π=3.14)Sol :
QUESTION 36
A heap of wheat is in the form of a cone whose diameter is 9m and height is 3.5m . Find its volume . How much canvas cloth will be required to cover the heap properly ?Sol :
QUESTION 37
A right triangle with sides 3cm and 4cm forming a right angle is revolved about its hypotenuse . Find the volume of the solid so obtained .Sol :
QUESTION 38
A right triangle with sides 5cm and 12cm forming a right angle is revolved about its hypotenuse . Find the volume of the solid so obtained.Sol :
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