Question

Rahul a 10th standard student makes a project on Corona virus in science for an
exhibition in his school. In this project, he picks a sphere which has a volume
38808 cm3 and 11 cylindrical shapes each of volume 1540 cm3with length 10cm.
(i) Diameter of the base of the cylinder is:
(a) 7 cm (b) 14 cm (c) 12 cm (d) 16 cm
(ii) Diameter of the sphere is:
(a) 40 cm (b) 42 cm (c) 21 cm (d) 20 cm
(iii) Total volume of the shape formed is:
(a) 85541 cm3 (b) 45738 cm3 (c) 24625 cm3 (d) 55748 cm3
(iv) Curved surface area of the one cylindrical shape is:
(a) 850 cm2 (b) 221 cm2 (c) 440 cm2 (d) 540 cm2
(v) Total area covered by cylindrical shapes on the surface area of the spheres
is:
(a) 1694 cm2 (b) 1580 cm2 (c) 1896 cm2 (d) 1470 cm2

Answer 1

Step-by-step explanation:

Volume of sphere =34πr3=38808

11×3528=34×722×r3

r3=21×21×21r=21

surface area =4πr2=74×22×(21)2=5544cm2

Answer 2

Concept Introduction:

Volume of cylinder= $1540$ cm$3$

Volume of sphere= $\frac{4}{3} \pi r$∧$3$

Curved surface area of the one cylindrical shape is = $2\pi rl$

Given:

Volume of sphere is $38808$cm$3$ and  cylindrical shapes each of volume $1540$cm$3$ with length $10$cm.

To Find:

We have to find the value of, diameter of cylinder and sphere, total volume of shape and curved surface area of cylinder.

Solution:

According to the problem,

(i) Volume of cylinder= $1540$ cm$3$

Now, V = $\pi r^{2} l$ = $1540$

⇒ $\frac{22}{7} * r^{2} * l = 1540$

⇒$r^{2} = \frac{154*7}{22}= 49$ ⇒ $r= 7$

∴$d = 14$

(ii)Volume of sphere= $\frac{4}{3} \pi r$∧$3$ $= 38808$

⇒ r∧$3$ = $\frac{38808*3*7}{4*22}$ = $9261$

⇒r = $21$

∴$d= 42$cm.

(iii) Total volume of shape = volume of sphere + $11$ x volume of cylinder

= $38808+11*1540 = 38808+16940=55748$ cm∧$3$.

(iv) Curved surface area of the one cylindrical shape is = $2\pi rl$ = $2*\frac{22}{7} *7*10=440$ cm∧$2$.

Final Answer:

The value of Diameter of sphere is $42cm$ Diameter of cylinder is $14cm$ total surface area of sphere is $55748$ cm∧$3$, curved surface area of cylinder is $440$cm∧$2$.

SPJ2