Class 10 maths Areas Related to Circles Hots Questions

Q 1 :

The radius of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is

2.1 cm
4.2 cm
3.1 cm
2.2 cm

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(1)

The diameter of the largest right circular cone that can be cut out from a cube of edge 4.2 cm.

$∴$ $2 r = 4.2 c m \Rightarrow r = 2.1 c m$

⇒ Radius of the largest right circular cone = 2.1 cm.

Q 2 :

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?

9 units
6 units
4.5 units
18 units

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(1)

Volume of hemisphere = Surface area of hemisphere

$\Rightarrow \frac{2}{3} π r^{3} = 3 π r^{2} \Rightarrow r = \frac{9}{2} u n i t s$

$∴$ d = 9 units

Q 3 :

Two identical solid hemispheres of equal base radius are stuck along their bases. The total surface area of the combination is

$π r^{2}$
$2 π r^{2}$
$3 π r^{2}$
$4 π r^{2}$

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(4)

The resultant solid will be a sphere of radius r whose total surface area is $4 π r^{2}$

Q 4 :

The sum of the length, breadth and height of a cuboid is $6 \sqrt{3}$ cm and the length of its diagonal is $2 \sqrt{3}$ cm. The total surface area of the cuboid is

$48 {cm}^{2}$
$72 {cm}^{2}$
$96 {cm}^{2}$
$108 {cm}^{2}$

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(3)

$Given: l + b + h = 6 \sqrt{3} cm$ ...(i)

$and the length of its diagonal = 2 \sqrt{3} cm \Rightarrow \sqrt{l^{2} + b^{2} + h^{2}} = 2 \sqrt{3}$

Squaring both sides, we get $l^{2} + b^{2} + h^{2} = 12$ ...(ii)

From eq. (i), ${(l + b + h)}^{2} = {(6 \sqrt{3})}^{2}$

$\Rightarrow l^{2} + b^{2} + h^{2} + 2 (l b + b h + h l) = 108$

$\Rightarrow 12 + 2 (l b + b h + h l) = 108$ $[From eq. (iii)] \Rightarrow 2 (l b + b h + h l) = 96$

Hence, total surface area of the cuboid is $96 {cm}^{2}$

Q 5 :

The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is :

$\frac{4 π}{3}$ cu cm
$\frac{5 π}{3}$ cu cm
$\frac{8 π}{3}$ cu cm
$\frac{2 π}{3}$ cu cm

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(4)

Radius of cone = 1 cm

Height of cone = 2 cm

Volume of cone $= \frac{1}{3} π r^{2} h = \frac{1}{3} π {(1)}^{2} \times 2 = \frac{2 π}{3} cu cm$

Q 6 :

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is:

1 : 1
1 : 4
2 : 3
3 : 2

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(3)

The total surface area of a sphere = $4 π r^{2}$

The surface area of one hemi-sphere = $3 π r^{2}$

$∴$ The total surface area of two hemi-spheres = $6 π r^{2}$

Required Ratio = $\frac{4 π r^{2}}{6 π r^{2}} = \frac{4}{6} = \frac{2}{3}$

Q 7 :

A cap is cylindrical in shape, surmounted by a conical top. If the volume of the cylindrical part is equal to that of the conical part, then the ratio of the height of the cylindrical part to the height of the conical part is :

1 : 2
1 : 3
2 : 1
3 : 1

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(2) 1 : 3

Q 8 :

A solid sphere is cut into two hemisphere. The ratio of the surface areas of sphere to that of two hemisphere taken together, is:

1 : 1
1 : 4
2 : 3
3 : 2

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(3)

Let r be the radius of sphere.

$S u r f a c e a r e a o f s p h e r e = 4 π r^{2} T o t a l s u r f a c e a r e a o f e a c h h e m i s p h e r e = C u r v e d s u r f a c e a r e a = 2 π r^{2}$

$B a s e a r e a = π r^{2} Total = 2 π r^{2} + π r^{2} = 3 π r^{2} S o f o r t w o h e m i s p h e r e s :$

$3 π r^{2} + 3 π r^{2} = 6 π r^{2} R e q u i r e d r a t i o : = \frac{4 π r^{2}}{3 π r^{2} + 3 π r^{2}} = \frac{4 π r^{2}}{6 π r^{2}} = \frac{4}{6} = \frac{2}{3}$

Q 9 :

The shape of a gilli, in the gilli-danda game (see figure), is a combination of:

two cylinders
a cone and a cylinder
two cones and a cylinder
two cylinders and a cone

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(3)

The shape of a gilli, in the gilli-danda game is a combination of two cones (ABC and DEF) and a cylinder (BDEC).

Q 10 :

If the surface area of a sphere is 616 cm², its diameter (in cm) is:

7
14
21
56

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(2)

$4 π r^{2} = 616 \Rightarrow r^{2} = 616 \times \frac{1}{4} \times \frac{7}{22} = 49 \Rightarrow r = 7 cm Diameter = 2 r = 2 \times 7 = 14 cm$

Topic Question Set

Q 1 :

The radius of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is

Q 2 :

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?

Q 3 :

Two identical solid hemispheres of equal base radius are stuck along their bases. The total surface area of the combination is

Q 4 :

The sum of the length, breadth and height of a cuboid is $6 \sqrt{3}$ cm and the length of its diagonal is $2 \sqrt{3}$ cm. The total surface area of the cuboid is

Q 5 :

The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is :

Q 6 :

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is:

Q 7 :

A cap is cylindrical in shape, surmounted by a conical top. If the volume of the cylindrical part is equal to that of the conical part, then the ratio of the height of the cylindrical part to the height of the conical part is :

Q 8 :

A solid sphere is cut into two hemisphere. The ratio of the surface areas of sphere to that of two hemisphere taken together, is:

Q 9 :

The shape of a gilli, in the gilli-danda game (see figure), is a combination of:

Q 10 :

If the surface area of a sphere is 616 cm², its diameter (in cm) is:

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Topic Question Set

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Q 10 :

If the surface area of a sphere is 616 cm², its diameter (in cm) is: