Question

Mr. Kumar, a Mathematics teacher brings some green colored clay in the classroom to teach

the topic ‘surface area and volume’. First, he forms a cylinder of radius 6cm and height 8cm

with the clay. Then he molds that cylinder into a sphere. Similarly, he molds the sphere into

other different shapes.

1.What is the volume of cylindrical shape formed?

(a) 268π cm3

(b) 288π cm^3


. (c) 36π cm^3


. (d) 48π cm^3

.

2. What will be the radius of Sphere formed by the same clay?

(a) 9cm (b) 10cm (c) 6cm (d) 8cm

3. What will be the difference between the curved surface areas of the above shapes?

(a) 40π cm^2


(b) 24π cm^2


(c) 48π cm^2


(d) 26π cm2


4.When the radius of cylinder increased by 1cm, what would be the volume of sphere formed

that time?

(a) 1212 cm^3


(b) 1222 cm^3


(c) 1132 cm^3


(d) 1232 cm^3

5. Amount of colored paper required to wrap the cylinder formed?

(a) 156 π cm^2


(b) 168 π cm^2


(c) 186 π cm^2


(d) 165 π cm^2

(please solve this and I'll mark you the brainliest)

Answer 1

1. (b)88pi c ^3

2.(c)6cm

3.(c)48pie cm^3

5.(b)168pie cm^2

Answer 2

Given,

The radius of cylinder=6cm

Height of cylinder=8cm

To find,

1. Volume of the cylindrical shape formed
2. Radius of a sphere formed by the same clay
3. Difference b/w the curved surface area
4. Volume of the sphere, if the radius of cylinder increased by 1 cm.
5. Amount of colored paper required to wrap the cylinder.

Solution,

1. Volume of cylinder= πr²h

= π×6×6×8

= 288πcm³ (option b)

2. Radius of sphere=?

since, the cylinder is molded into a sphere,

therefore, the volume of the cylinder= volume of the sphere

⇒ πr²h=4/3πr³

⇒π×r×r×h=4/3×π×r×r×r

⇒h=4/3r

⇒8=4/3×r

⇒r=6cm. (option c)

3.  The difference between the curved surface area of both the shapes

C.S.A of cylinder=2πrh

C.S.A of sphere=4πr²

⇒2πrh - 4πr² = 2×π×6×8 - 4×π×6×6

⇒144π - 96π = 48π

Therefore, difference=48πcm². (option c)

4. When the radius of the cylinder increased by 1cm

volume of sphere=1232cm³

5. Amount of colored paper required to wrap the cylinder

168πcm². ( option b )