Total surface area of a cone= .........

1

(a)

\(\pi rl+\pi { r }^{ 2 }\quad or\quad \pi r(l+r)\)

Frustum is a latin word, meaning ............

1

(a)

piece cut off

The slant height of the frustum of cone (l) = ................

1

(a)

\(Slant\ height\ (l)=\sqrt { { h }^{ 2 }+{ \left( R-r \right) }^{ 2 } } \)

Toy (Latto) is a solid which is a combination of ............. and .............

1

(a)

Cone and hemisphere.

Volume of a spherical shell = ...........

1

(a)

\(\frac { 4 }{ 3 } \pi \left( { R }^{ 3 }-{ r }^{ 3 } \right) cubic\quad units.\)

Volume of the frustum of the cone is \(\frac { 1 }{ 3 } \pi \left( { R }^{ 2 }+{ r }^{ 2 }+Rr \right) \times h.\)

1

(a) False

(b) True

Common part of two or more combined solids is excluded, while calculating the volume of the combinations.

1

(a) False

(b) True

If we double the radius of a hemisphere, its urface area will also be doubled.

1

(a) True

(b) False

A cuboid has eight faces

1

(a) True

(b) False

All faces of a cuboid must be rectangular.

1

(a) True

(b) False

A conical military tent having diameter of the base 24m and slant height of the tent is 13m, find the curved surface area cone.\([\pi={22\over7}]\)

1

(a)

Diameter of tent=24m radius=12m
Slant height=13m
Curved surface area \(=\pi rl={22\over7}\times 12\times ={3432\over7}m^2\)

Find the radius of a sphere whose surface area is 154cm²

1

(a)

Surface area=154 cm²
\(\Rightarrow\ \ 4\pi r^2=154\ \ \Rightarrow r^2={154\times7\over4\times22}\)
\(\Rightarrow\ \ r=\sqrt{7\times7\over2\times2}={7\over2}=3.5\)

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.\([\pi={22\over7}]\)

1

(a)

Base radius of Joker's cap=7cm; slant height=25cm
Curved surface area \(=\pi rl={22\over7}\times7\times25=550cm^2\)

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 \(4\pi rh+4\pi r^2\)

1

(a)

False.

Total surface area of the figure = \(\frac { 2\pi { r }h+\pi { r }^{ 2 } }{ upper\quad cylinder } +\frac { \pi { r }^{ 2 }+2\pi { r }h }{ lower\quad cylinder } =4\pi { r }h+2\pi { r }^{ 2 }\) 

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.

1

(a)

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