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Maths 1 Marks Question

Surface Area And Volume of Sphere · CBSE STD 9 (CBSE - English Medium). 22 questions.

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Question 11 Mark
Find the surface area of a sphere of diameter:$3.5\ cm$
Answer
Given Diameter $= 3.5\ cm$
Radius $=\frac{\text{Diameter}}{2}$
$=\frac{3.5}{2}=1.75\text{cm}$
Surface area $4\pi\text{r}^2$
$=4\times\frac{22}{7}\times(1.75)^2$
$=38.5\text{cm}^2$
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Question 21 Mark
Find the volume of a sphere whose radius is: $2\ cm.$
Answer
Radius $(r) = 2cm$
Therefore volume $=\frac{4}{3\pi\text{r}^3}$
$=\frac{4}{3}\times\frac{22}{7}\times(2)^3$
$=33.52\text{cm}^3$
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Question 31 Mark
Find the surface area of a sphere of diameter:$21\ cm$
Answer
Given Diameter $= 21\ cm$ Radius $=\frac{\text{Diameter}}{2}$
$=\frac{21}{2}=10.5\text{cm}$ Surface area $4\pi\text{r}^2$
$=4\times\frac{22}{7}\times(10.5)^2$
$=1386\text{cm}^2$
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Question 41 Mark
Find the volume of a sphere whose radius is:$10.5\ cm.$
Answer
Radius $(r) = 10.5cm$
Therefore volume $=\frac{4}{3\pi\text{r}^3}$
$=\frac{4}{3}\times\frac{22}{7}\times(10.5)^3=4851\text{cm}^2$
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Question 51 Mark
Find the volume of a sphere whose radius is: $3.5\ cm$
Answer
Radius $(r) = 3.5\ cm$ Therefore volume $=\frac{4}{3\pi\text{r}^3}$ $=\frac{4}{3}\times\frac{22}{7}\times(3.5)^3$ $=179.666\text{cm}^3$
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Question 61 Mark
Find the volume of a sphere whose diameter is: $14\ cm.$
Answer
Diameter $= 14\ cm$,
Radius (r) $=\frac{14}{2}=7\text{cm}$
Therefore volume $=\frac{4}{3\pi\text{r}^3}$
$=\frac{4}{3}\times\frac{22}{7}\times(7)^2=1437.33\text{cm}^3$
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Question 71 Mark
Find the surface area of a sphere of radius: $10.5\ cm$
Answer
Given Radius $= 15.5\ cm$
Surface area $=4\pi\text{r}^2$
$=4\times\frac{22}{7}\times(10.5)^2$
$=1386\text{cm}^2$
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Question 81 Mark
Find the surface area of a sphere of radius:$14\ cm$
Answer
Given radius $= 14\ cm$
Surface area $=4\pi\text{r}^2$
$=4\times\frac{22}{7}\times(14)^2$
$=2464\text{cm}^2$
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Question 91 Mark
Find the surface area of a sphere of radius: $5.6\ cm$
Answer
radius Given $= 5.6\ cm$
Surface area $=4\pi\text{r}^2$
$=4\times\frac{22}{7}\times(5.6)^2$
$=394.24\text{cm}^2$
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Question 101 Mark
Find the surface area of a sphere of diameter:
$14\ cm$
Answer
Given Diameter $= 14\ cm$
Radius $=\frac{\text{Diameter}}{2}$
$=\frac{14}{2}=7\text{cm}$
Surface area $=4\pi\text{r}^2$
$=4\times\frac{22}{7}\times(7)^2$
$=616\text{cm}^2$
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Question 111 Mark
Find the volume of a sphere whose diameter is:
$3.5\ dm$
Answer
Diameter $= 3.5\ dm$, Radius $(r) 3.52 = 1.75\ dm$
Therefore volume $=\frac{4}{3\pi\text{r}^3}$
$=\frac{4}{3}\times\frac{22}{7}\times(1.75)^3$
$= 22.46dm^3$
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Question 121 Mark
Find the volume of a sphere whose diameter is:$2.1m$
Answer
Diameter $= 2.1\ m,$
Radius (r) $=\frac{2.1}{2}=1.05\text{m}$
Therefore volume $=\frac{4}{3\pi\text{r}^3}$
$=\frac{4}{3}\times\frac{22}{7}\times(1.05)^3=4.851\text{m}^3$
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Question 131 Mark
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
Answer
$6: \pi$
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Question 141 Mark
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.
Answer
3 cm
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Question 151 Mark
If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.
Answer
14 cm
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Question 161 Mark
If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.
Answer
32r
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Question 171 Mark
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
Answer
2541
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Question 191 Mark
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
Answer
$154 m^2$
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