Sphere and Its Surface Area

Q. If the heights of two right circular cones are in the ratio 1 : 2 and the perimeters of their bases are in the ratio 3 : 4, what is the ratio of their volumes?

Q.

The volumes of two spheres are in the ratio 27 : 64. What is the ratio of their radii?

Q.

The surface area of a sphere is $5544c{m}^2$, find its diameter.

Q. The internal and external radii of a hollow hemispherical vessel are 12 cm and 12.5 cm respectively. If the cost for painting $1c{m}^2$ of the surface area is ₹0.05, then the total approximate cost of painting the vessel all over is $[use\pi =\frac{22}{7}]$

1. ₹96.28
2. ₹90.15
3. ₹84.45
4. ₹92.45

Q.

The surface area of a solid sphere is increased by 21% without changing its shape.Find the percentage increase in its:

(i) radius (ii) volume

Q. The surface area of a sphere is 2464 cm². If its radius be doubled, then what will be the surface area of the new sphere?

Q. The surface area of a sphere is 616 cm² . Find its radius.

Q. Choose the correct answer of the following question:

If the radius of a sphere becomes 3 times, then its volume will become

(a) 3 times (b) 6 times (c) 9 times (d) 27 times [CBSE 2011]

Q. The surface areas of two spheres are in the ratio of 4 : 25. Find the ratio of their volumes.

Q.

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

$\begin{array}{cc}Assertion\left(A\right)& Reason\left(R\right)\\ Ifthevolumesoftwospheresare& Volumeofaspheres=\frac{4}{3}\pi R^3.\\ intheratio27:8thentheirsurface& \\ areasareintheratio3:2& Surfaceareaofasphere=4\pi R^2.\end{array}$

The correct answer is (a) / (b) / (c) / (d).

Q.

The radius of sphere is r cm. It is divided into two equal parts. Find the whole surface of two parts.

Q.

The volume of a solid hemisphere is $1152\mathrm{\pi }$${\text{cm}}^3$. Find its curved surface area ?

Q.

Find the surface area of a sphere whose radius is 21 cm.

Q.

The curved surface area of a shpere is 5544 $c{m}^3$. Find its volume.

Q. Two spheres of same material are heated up to same temperature and then allowed to cool in same surrounding. If their radii are in the ratio of 4:7 then ratio of their initial rate of cooling is? 1) 2:7 2) 7:2 3) 4:7 4) 7:4

Q.

A surahi is a combintion of

(a) a sphere and a cylinder

(b) a hemisphere and a cylinder

(c) a cylinder and a cone

(d) two hemispheres

Q.

The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is

(a) 9 : 16 (b) 16 : 9 (c) 3 : 4 (d) 4 : 3

Q.

Do you think the cross-section of a sphere are always circles ? What is different about each cross - section ?

Q.

Find the total surface area of cubes having the following sides $5\mathrm{cm}$

Q.

The surface area of a sphere is 2464 $c{m}^2.$ If its radius be doubled, what will be the surface area of the new sphere?

Q.

What is the area of the hemisphere?

Q.

Find the surface area of a sphere whose radius is 21 cm.

Q.

Find the total surface area of cubes having the following sides $3\mathrm{cm}$

Q. Volumes of two spheres are in the ratio 64 ; 27 . The ratio of their surface areas is
(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9

Q. The radii of two spheres $s_1$ and $s_2$ are in the ratio 4:3. If $s_1$ and $s_2$ are melted and converted into a new sphere, then the ratio of volumes of sphere $s_1$ and the new sphere is

1. 64:91
2. 27:91
3. 27:64
4. 4:7

Q. Choose the correct answer of the following question:

The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is

(a) 64 : 27 (b) 16 : 9 (c) 4 : 3 (d) 16³ : 9³ [CBSE 2013C]

Q. The surface area of the biggest sphere, which can fit in a cube of edge 8 cm is equal to

1. $\frac{704}{7}c{m}^2$
   
2. $\frac{1408}{7}c{m}^2$
   
3. $\frac{2816}{7}c{m}^2$
   
4. $\frac{1800}{7}c{m}^2$
   

Q. If volumes of two spheres are in the ratio 64 : 27, then the ratio of their surface areas is:

1. 4 : 3
2. 9 : 16
3. 3 : 4
4. 16 : 9

Q. Assertion (A)
If the volumes of two spheres are in the ratio 27 : 8, then their surface areas are in the ratio 3 : 2.

Reason (R)
Volume of a sphere = $\frac{4}{3}\mathrm{\pi }{R}^3$
Surface area of a sphere = $4\mathrm{\pi }{R}^2$

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q.

A plumbline (Sahul) is the combination of:-

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