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Published on: 12/06/2021
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Questions + Answers key
Take MCQ Maths Test1.
2.
A sphere, a cylinder and a cone are of the same radius, where as cone and cylinder are of same height. Find the ratio of their curved surface areas.

3.
If the base area of a hemispherical solid is 1386 sq. metres, then find its total surface area?
4.
The radius of a spherical balloon increases from 12 cm to 16 cm as air being pumped into it. Find the ratio of the surface area of the balloons in the two cases.
5.
Find the diameter of a sphere whose surface area is 154 m2.
6.
If the total surface area of a cone of radius 7cm is 704 cm2, then find its slant height.
7.
If one litre of paint covers 10 m2, how many litres of paint is required to paint the internal and external surface areas of a cylindrical tunnel whose thickness is 2 m, internal radius is 6 m and height is 25 m.

8.
A garden roller whose length is 3 m long and whose diameter is 2.8 m is rolled to level a garden. How much area will it cover in 8 revolutions?
9.
The curved surface area of a right circular cylinder of height 14 cm is 88 cm2 . Find the diameter of the cylinder.
10.
A cylindrical drum has a height of 20 cm and base radius of 14 cm. Find its curved surface area and the total surface area.
1.
2.
Required Ratio = C.S.A. of the sphere: C.S.A. of the cylinder : C.S.A. of the cone
\(4\pi { r }^{ 2 }:2\pi rh:\pi rl,\ (l=\sqrt { { r }^{ 2 }+{ h }^{ 2 } } =\sqrt { { 2r }^{ 2 } } =\sqrt { 2r } units)\)
\(=4:2:\sqrt { 2 } =2\sqrt { 2 } :\sqrt { 2 } :1\).
3.
Let r be the radius of the hemisphere.
Given that, base area = \(\pi\)r2 = 1386 sq. m
T.S.A. = 3 \(\pi\)r2 sq.m
= 3 x 1386 = 4158
Therefore, T.S.A. of the hemispherical solid is 4158 m2.
4.
Let r1 and r2 be the radii of the balloons.
Given that, \(\frac { { r }_{ 1 } }{ { r }_{ 2 } } =\frac { 12 }{ 16 } =\frac { 3 }{ 4 } \)
Now, ratio of C.S.A. of balloons \(=\frac { 4\pi { r }_{ 1 }^{ 2 } }{ 4\pi { r }_{ 2 }^{ 2 } } =\frac { { r }_{ 1 }^{ 2 } }{ { r }_{ 2 }^{ 2 } } ={ \left( \frac { { r }_{ 1 } }{ { r }_{ 2 } } \right) }^{ 2 }={ \left( \frac { 3 }{ 4 } \right) }^{ 2 }=\frac { 9 }{ 16 } \)
Therefore, ratio of C.S.A. of balloons is 9:16.
5.
Let r be the radius of the sphere. Given that, surface area of sphere = 154 m2
4\(\pi\)r2 = 154
\(4\times \frac { 22 }{ 7 } \times { r }^{ 2 }=154\)
gives \({ r }^{ 2 }=154\times \frac { 1 }{ 4 } \times \frac { 7 }{ 22 } \)
hence, \({ r }^{ 2 }=\frac { 49 }{ 4 } \)We get r = \(\frac{7}{2}\)
Therefore, diameter is 7 m
6.
Given that, radius r = 7 cm
Now, total surface area of the cone = \(\pi\)r(l + r)sq. units
T.S.A = 704 cm2
704 = \(\frac{22}{7}\times7(l+7)\)
32 = l + 7 implies l = 25 cm
Therefore, slant height of the cone is 25 cm.
7.
Given that, height h = 25 Given that, height h = 25 m; thickness = 2 m.
internal radius r = 6 m
Now, external radius R = 6 + 2 = 8m
C.S.A. of the cylindrical tunnel = C.S.A. of the hollow cylinder
C.S.A. of the hollow cylinder = 2\(\pi\)(R + r)h sq.units
\(2\times \frac { 22 }{ 7 } (8+6)\times 25\)
Hence, C.S.A. of the cylindrical tunnel = 2200 m2
Area covered by one litre of paint = 10 m2
Number of litres required to paint the tunnel \(=\frac { 2200 }{ 10 } =220\)
Therefore, 220 litres of paint is needed to paint the tunnel.
8.
Given that, diameter d = 2.8 m and height = 3 m
radius r = 1.4 m
Area covered in one revolution = curved surface area of the cylinder
= 2\(\pi\)rh sq. units
\(2\times \frac { 22 }{ 7 } \times 1.4\times 3=26.4\)
Area covered in 1 revolution = 26.4 m2
Area covered in 8 revolutions = 8 x 26.4 = 211.2
Therefore, area covered is 211.2 m2
9.
Given that, C.S.A. of the cylinder = 88 sq. cm
2\(\pi\)rh = 88
\(2\times \frac { 22 }{ 7 } \times 14=88\) (given h = 14cm)
2r = \(\frac { 88\times 7 }{ 22\times 14 } =2\)
Therefore, diameter = 2 cm
10.
Given that, height of the cylinder h = 20 cm ; radius r =14 cm
Now, C.S.A. of the cylinder = 2p\(\pi\)h sq. units
C.S.A. of the cylinder = \(2\times \frac { 22 }{ 7 } \times 14\times 20=2\times 22\times 2\times 20\)
T.S.A. of the cylinder \(=2\pi r(h+r)\)sq.units
\(=2\times \frac { 22 }{ 7 } \times 14\times (20+14)=2\times \frac { 22 }{ 7 } \times 14\times 34\)
= 2992 cm2
Therefore, C.S.A. = 1760 cm2 and T.S.A. = 2992 cm2
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Tamilnadu Stateboard 10th Standard Subjects
Tamilnadu Stateboard Standards