Question

Science Project Arun 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 volume 38808 cm³ and 11 cylindrical shapes, each of volume 1540 cm³ with length 10 cm. Based on the above information, answer the following questions. (i) Diameter of the base of the cylinder is (a) 7 cm (b) 14 cm (ii) Diameter of the sphere is (a) 40 cm (b) 42 cm (iii) Total volume of the shape formed is (a) 85541 cm³ (b) 45738 cm³ (c) 12 cm (c) 21 cm (c) 24625 cm³ (iv) Curved surface area of the one cylindrical shape is (a) 850 cm² (b) 221 cm² (c) 440 cm² (d) 16 cm (d) 20 cm (d) 55748 cm³ (d) 540 cm² (v) Total area covered by cylindrical shapes on the surface of sphere is (a) 1694 cm² (b) 1580 cm² (c) 1896 cm² (d) 1470 cm²​

Answer 1

Answer:

a,d,c,b,a answers I think

Answer 2

Answer:

(i) The diameter of the base of the cylinder is 14 cm

(ii) The diameter of the sphere is 42 cm

(iii) The total volume of the shape is 55748 cm³

(iv) The curved surface area of the one cylindrical shape is 440cm²

(v) The total area covered by cylindrical shapes on the surface of sphere is 1694 cm²

Step-by-step explanation:

Given:

Volume of sphere = 38808 cm³

No. of cylindrical shapes = 11

Volume of 1 cylinder = 1540 cm³

Length of cylinder = 10 cm

(i) We know that Volume of cylinder = πr²h

where r is radius of the base

and h is the height of the cylinder

=> 1540 =  $\frac{22}{7}$ * r² * 10

=> 49 =  r²

=> r = ± 7

=> r = 7 cm

We know diameter = 2 * r

                                = 2*7

                                = 14 cm

Therefore, the diameter of the base of the cylinder is 14 cm

(ii) We know that volume of a sphere = $\frac{4}{3}$ * πr³

=> 38808 =  $\frac{4}{3}$  *  $\frac{22}{7}$ * r³

=> 9261 =  r³

=> r = 21

We know diameter = 2 * r

                                = 2*21

                                = 42 cm

Therefore, the diameter of the sphere is 42 cm

(iii) Total volume = Volume of sphere + Volume of 11 cylinders

                            = 38808 cm³ + 11 * 1540 cm³

                            = 38808 cm³ + 16940 cm³

                            = 55748 cm³

Therefore, the total volume of the shape is 55748 cm³

(iv) We know that Curved surface area of cylinder = 2πrh  

                                                                                   = 2 * $\frac{22}{7}$ * 7 * 10

                                                                                   = 440cm²

Therefore, the curved surface area of the one cylindrical shape is 440cm²

(v) Total area covered by cylindrical shapes on the surface of sphere =

Area of the base of 11 cylinders

= 11 * πr²

= 11 * $\frac{22}{7}$ * 7²

= 1694 cm²

Therefore, the total area covered by cylindrical shapes on the surface of sphere is 1694 cm²