Q77 of 227 Page 917

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

Assertion (A): A hemisphere of radius 7 cm is to be painted outside on the surface. The total cost of painting at Rs 5 per cm2 is Rs 2300.


Reason (R): The total surface area of a hemisphere is 3πr2.

Assertion is wrong and Reason is correct.


Explanation:


Assertion (A):


Given: A hemisphere of radius 7 cm.


Total surface area of the hemisphere is: 3πr2


Let S be the TSA of the hemisphere.


S = 3πr2 = 3π(7)2


S = 462cm2


The total cost to pain it: 462 × 5 = Rs 2310


Reason(R):


The total surface area of a hemisphere is 3πr2.


Assertion is wrong and Reason is correct.

More from this chapter

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75

Match the following columns:























Column I



Column II



(a) The radii of the circular ends of a bucket in the form of frustum of a cone of height 30 cm are 20 cm and 10 cm respectively. The capacity of the bucket is ….. cm3. [Take π = 22/7]



(p) 2418π



(b) The radii of the circular ends of a conical bucket of height 15 cm are 28 and 20 cm respectively. The slant height of the bucket is …. cm.



(q) 22000



(c) The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. The total surface area of the bucket is …. Cm2.



(r) 12



(d) Three solid metallic sphere of radii 3 cm, 4 cm and 5 cm are melted to form a single solid sphere. The diameter of the resulting sphere is … cm.



(s) 17


76

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

Assertion (A): If the radii of the circular ends of a bucket 24 cm high are 15 cm and 5 cm respectively, then the surface area of the bucket is 545 π cm2.


Reason (R): If the radii of the circular ends of the frustum of a cone are R and r respectively and its height is h, then its surface area is π {R2 + r2 + l(R - r)},where l2 = h2 + (R –r)2.

78

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

Assertion (A): The number of coins 1.75 cm in diameter and 2 mm thick from a melted cuboid (10 cm × 5.5 cm × 3.5 cm) is 400.


Reason (R): Volume of a cylinder of base radius r and height h is given by V= (πr2h) cubic units. And, area of a cuboid = (l × b × h) cubic units.

79

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

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


Reason (R): Volume of a sphere .


Surface area of a sphere = 4πR2.