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Which of the following statement(s) given below is / are TRUE? A: A large solid cube is melted and casted into 3375 small cubes of side 1.6 cm, then side of large cube is 24 cm. B: Total surface area of a hemisphere of total volume 2425.5 cm3 is 693 cm2. C: Height of a cylinder of radius 14 cm and total surface area 2288 cm is 12 cm2. 

Which of the following statement(s) given below is / are TRUE? A: A large solid cube is melted and casted into 3375 small cubes of side 1.6 cm, then side of large cube is 24 cm. B: Total surface area of a hemisphere of total volume 2425.5 cm3 is 693 cm2. C: Height of a cylinder of radius 14 cm and total surface area 2288 cm is 12 cm2.  Correct Answer A and C

GIVEN:

Three statements.

CONCEPT:

Mensuration

FORMULA USED:

Volume of cube = S3

Total volume of hemisphere = (2 / 3)πR3

Total surface area of hemisphere = 3πR2

Total surface area of cylinder = 2πR(H + R)

CALCULATION:

A:

Volume of large solid cube = 3375 × Volume of a small cube

a3 = 3375 × 1.63

⇒ a3 = 13824

⇒ a = 24

Side of large cub = 24 cm

B:

Let radius of hemisphere = R

Total volume of hemisphere = (2 / 3) × (22 / 7) × R3 = 2425.5

R3 = 1157.625

⇒ R = 10.5

Total surface area of hemisphere = 3 × (22 / 7) × R2

= 3 × (22 / 7) × 10.52

= 1039.5 cm2

C:

Let height of cylinder = H

Total surface area = 2288

2 × (22 / 7) × 14 × (14 + H) = 2288

⇒ 14 + H = 26

⇒ H = 12

Height of cylinder = 12 cm

Hence, only statements A and C are TRUE.

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