Question 11 Mark
A right circular cylinder just encloses a sphere of radius r units. Calculate the surface area of the sphere
Answer
View full question & answer→Surface area of sphere $=4 \pi r^2$ sq.units
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[1 Mark Questions]
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Question 21 Mark
A right circular cylinder just encloses a sphere of radius r units. Calculate the ratio of the areas of the sphere and cylinder
Answer
View full question & answer→Surface area of sphere $=4 \pi r^2$ sq.units
C.S.A of cylinder
$=2 \pi r \times h$
$=2 \pi r \times 2 r$
$=4 \pi r^2$ sq.units
Ratio $=\frac{4 \pi r^2}{4 \pi r^2}=1: 1$
C.S.A of cylinder
$=2 \pi r \times h$
$=2 \pi r \times 2 r$
$=4 \pi r^2$ sq.units
Ratio $=\frac{4 \pi r^2}{4 \pi r^2}=1: 1$
Question 31 Mark
If the ratio of radii of two spheres is 4 : 7, find the ratio of their volumes.
Answer
View full question & answer→Let the ratio of their radii is $r_1: r_2$
$
r_1: r_2=4: 7
$
Ratio of their volumes
$
\begin{aligned}
& V _1: V _2=\frac{4}{3} \pi r _1^3: \frac{4}{3} \pi r _2^3 \\
& = r _1^3: r _2^3 \\
& =4^3: 7^3
\end{aligned}
$
Ratio of their volumes $=64: 343$
$
r_1: r_2=4: 7
$
Ratio of their volumes
$
\begin{aligned}
& V _1: V _2=\frac{4}{3} \pi r _1^3: \frac{4}{3} \pi r _2^3 \\
& = r _1^3: r _2^3 \\
& =4^3: 7^3
\end{aligned}
$
Ratio of their volumes $=64: 343$
Question 41 Mark
The volumes of two cones of same base radius are $3600 cm^3$ and $5040 cm^3$. Find the ratio of heights.
Answer
View full question & answer→Let the radius of the two cones be ' $r$ '
Let the height of the two cones be $h _1$ and $h _2$
$
\begin{aligned}
& \text { Ratio of their volumes }=3600: 5040 \ldots(\div 10) \\
& \frac{1}{3} \pi r ^2 h _1: \frac{1}{3} \pi r ^2 h _2=360: 504 \ldots(\div 4) \\
& h _1: h _2=90: 126 \ldots(\div 3) \\
& =30: 42 \ldots(\div 3) \\
& =10: 14 \ldots(\div 2) \\
& h _1: h _2=5: 7
\end{aligned}
$
Ratio of heights $=5: 7$
Let the height of the two cones be $h _1$ and $h _2$
$
\begin{aligned}
& \text { Ratio of their volumes }=3600: 5040 \ldots(\div 10) \\
& \frac{1}{3} \pi r ^2 h _1: \frac{1}{3} \pi r ^2 h _2=360: 504 \ldots(\div 4) \\
& h _1: h _2=90: 126 \ldots(\div 3) \\
& =30: 42 \ldots(\div 3) \\
& =10: 14 \ldots(\div 2) \\
& h _1: h _2=5: 7
\end{aligned}
$
Ratio of heights $=5: 7$