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Published on: 29/08/2019
Surface Areas and Volumes
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1.
There are two cones.The curved surface area of one is twice that of the other.The slant height of the latter is twice that of the former.Find ratio their radii.
2.
A solid cylinder of radius r and height h is placed over other cylinder of same height and radius.The surface area of the shape so formed is \(4\pi rh+4\pi r^2\)
3.
A joker's cap is in the form of a right circular cone of base radius 7cm and the slant height is 25cm.Find the area of the cap.\([\pi={22\over7}]\)
4.
Find the radius of a sphere whose surface area is 154cm2
5.
A conical military tent having diameter of the base 24m and slant height of the tent is 13m, find the curved surface area cone.\([\pi={22\over7}]\)
6.
Volume of a spherical shell = ...........
7.
Toy (Latto) is a solid which is a combination of ............. and .............
8.
The slant height of the frustum of cone (l) = ................
9.
Frustum is a latin word, meaning ............
10.
Total surface area of a cone= .........
11.
All faces of a cuboid must be rectangular.
12.
A cuboid has eight faces
13.
If we double the radius of a hemisphere, its urface area will also be doubled.
14.
Common part of two or more combined solids is excluded, while calculating the volume of the combinations.
15.
Volume of the frustum of the cone is \(\frac { 1 }{ 3 } \pi \left( { R }^{ 2 }+{ r }^{ 2 }+Rr \right) \times h.\)
16.
Surface area of a cuboid
17.
Total surface area of the frustum of the cone
18.
Volume of the frustum of a cone
19.
Total surface area of a hemisphere
20.
Volume of hollow cylinder
1.
Let C1, C2 be the C.S.A of two cones.
C1= 2C2
2l1=l2,l1,l2 be the slant heights and r1, r2 be the radii of two cones:
\(\Rightarrow\) C1 = 2C2 [Given]
\(\Rightarrow\) \(\pi\)r1l1 = 2\(\pi\)r2l2
\(\Rightarrow\) r1l1 = 2r2 2l1
\(\Rightarrow\) r1 = 4r2
r1:r2 = 4:1
2.
False.
Total surface area of the figure = \(\frac { 2\pi { r }h+\pi { r }^{ 2 } }{ upper\quad cylinder } +\frac { \pi { r }^{ 2 }+2\pi { r }h }{ lower\quad cylinder } =4\pi { r }h+2\pi { r }^{ 2 }\)
3.
Base radius of Joker's cap=7cm; slant height=25cm
Curved surface area \(=\pi rl={22\over7}\times7\times25=550cm^2\)
4.
Surface area=154 cm2
\(\Rightarrow\ \ 4\pi r^2=154\ \ \Rightarrow r^2={154\times7\over4\times22}\)
\(\Rightarrow\ \ r=\sqrt{7\times7\over2\times2}={7\over2}=3.5\)
5.
Diameter of tent = 24m radius = 12m
Slant height=13m
Curved surface area =\(\pi r l=\frac{22}{7} \times 12 \times=\frac{3432}{7} m^2\)
6.
( )
\(\frac { 4 }{ 3 } \pi \left( { R }^{ 3 }-{ r }^{ 3 } \right) cubic\quad units.\)
7.
( )
Cone and hemisphere.
8.
( )
\(Slant\ height\ (l)=\sqrt { { h }^{ 2 }+{ \left( R-r \right) }^{ 2 } } \)
9.
( )
piece cut off
10.
( )
\(\pi rl+\pi { r }^{ 2 }\quad or\quad \pi r(l+r)\)
11.
(b)
12.
(b)
13.
(b)
14.
(a)
15.
(a)
16.
( )
2(lb+bh+hl)
17.
( )
\(\pi { r }^{ 2 }+\pi { R }^{ 2 }+\pi \left( R+r \right) l\)
18.
( )
\(\frac { 1 }{ 3 } \pi { (R }^{ 2 }+{ r }^{ 2 }+Rr)h\)
19.
( )
\(3\pi { r }^{ 2 }\)
20.
( )
\(\pi { R }^{ 2 }h-\pi { r }^{ 2 }h\)
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