Sphere and Hemisphere and Its Surface Area

Q. Question 14
A medicine – capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. the capacity of the capsule is
(A) $0.36c{m}^3$
(B) $0.35c{m}^3$
(C) $0.34c{m}^3$
(D) $0.33c{m}^3$

Q.

Find the change in surface area of a sphere if its radius is increased 4 times.

1. Surface area increases 2 times

2. Surface area increases 16 times

3. Surface area decreases 16 times

4. Surface area decreases 2 times

Q. If the area of base of a cone is 49$\pi m^2$ and its CSA is 175$\pi m^2$, then its height is __ m.

1. 24

Q. A Shpere and Hemisphere has radius '$r$'. (TSA - total surface area; CSA - Curved surface area)

1. $4\pi r^2$
2. $2\pi r^2$
3. $3\pi r^2$

Q. If surface area of a sphere of radius “R” is equal to curved surface area of a hemisphere of radius “r”, what is the value of R/r ?

1. $\frac{1}{2}$
2. $\frac{1}{\sqrt{2}}$
3. 2
4. $\sqrt{2}$

Q.

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder (in cm).

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Q. Surface area of a sphere of radius r is $4\pi r^2$.

1. False
2. True

Q. Question 1
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Q.

The diameter of the moon is approximately one fourth the diameter of the earth. Find the ratio of their surface areas.

Q.

Question 1
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Q. A symbolic solid sphere has to be painted to stop it from corroding. If the cost of painting at ₹ 100/m${}^2$ is ₹ 15, 400 then the radius of the sphere is _____. Take$(\pi =\frac{22}{7})$

1. 7 m
2. 3.5 m
3. 2.5 m
4. 2.5 cm

Q.

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder (in cm).

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Q. The increase in the total surface area of a sphere of Radius $R$ when it is cut to make two hemispheres of same Radius will be equal to:

1. $5\pi R^2$
2. $4\pi R^2$
3. $3\pi R^2$
4. $2\pi R^2$

Q. A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surface area will be:

1. $1:\sqrt{2}$
2. $\sqrt{2}:1$
3. $\sqrt{3}:1$
4. $2:1$

Q.

The innder diameter of a glass is 7 cm and it has a raised portion in the bottom in the shape of a hemisphere, as shown in the figure. If the height of the glass is 16 cm, find the apparent capacity and the actual capacity of the glass.

Q. You are holding a spherical ball of radius 3.5 cm in your fist. You observe that 30% of area is uncovered. Then find the area of the ball uncovered. (Take $\pi =\frac{22}{7}$)

1. $46.2{\text{cm}}^2$
2. $26.2{\text{cm}}^2$
3. $36.2{\text{cm}}^2$
4. $16.2{\text{cm}}^2$

Q. The total surface area of a hemisphere having radius r is _____ .

1. $4\pi r^2$
2. $3\pi r^2$
3. $2\pi r^2$
4. $\frac{5}{2}\left(\pi r^2\right)$

Q. Total surface area of a hemisphere with radius ${}^{\prime }{r}^{\prime }$ units, will be equal to

1. $4\pi r^2$
2. $3\pi r^2$
3. $\frac{4}{3}\pi r^3$
4. $\frac{2}{3}\pi r^3$

Q. If the radius of a sphere is 12 cm, then its surface area will be .
(Take $\pi =3.14)$

1. $1808.64c{m}^2$
2. $2808.64c{m}^2$
3. $1800.64c{m}^2$
4. $1900c{m}^2$

Q.

The curved surface area of a sphere of radius 5 cm is ____ sq cm.

1. 10π

2. 20π

3. 80π

4. 100π

Q.

In a circus, a motorcyclist performs his stunts inside a hollow sphere. The thickness of the sphere is negligible. If the diameter of the hollow sphere is 14 m, then find the area available for the motorcyclist to perform his stunts.
$(use\pi =\frac{22}{7})$

1. 516 $m^2$

2. 616 $m^2$

3. 586 $m^2$

4. 486 $m^2$

Q. If the radius of a sphere is 12 cm, then its surface area will be .
(Take $\pi =3.14)$

1. $1808.64c{m}^2$
2. $2808.64c{m}^2$
3. $1800.64c{m}^2$
4. $1900c{m}^2$