Question

31. A girl makes a cylindrical sand castle 16 cm
in diameter and 12 cm high on the beach. If
the same sand is moulded into circular discs 4cn in diameter and 3cm thick how many discs can be made ​

Answer 1

Step-by-step explanation:

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Answer 2

GIVEN:

• Diameter of the cylindrical castle = 16 cm
• Height of the cylindrical castle = 12 cm
• Diameter of the circular discs = 4 cm
• Thickness (Height) of the circular discs = 3 cm

TO FIND:

• How many discs can be made ?

SOLUTION:

Diameter of the cylindrical castle = 16 cm

$\bf{ Radius = \dfrac{Diameter}{2} = \cancel\dfrac{16}{2}}$

$\bf{\star \: Radius = 8 \: cm \: \star}$

Diameter of the circular discs = 4 cm

$\bf{ Radius = \dfrac{Diameter}{2} = \cancel\dfrac{4}{2}}$

$\bf{\star \: Radius = 2 \: cm \: \star}$

We have given that, the cylindrical castle is moulded into circular discs:-

$\Large{\boxed{\bf{\star \: \pi r^2 h = \pi R^2 h \: \star}}}$

According to question:-

$\rm{\dashrightarrow \cancel{\pi} r^2 h = \cancel{\pi}R^2 h }$

$\rm{\dashrightarrow (8)^2 \: 12 = (2)^2 \times 3 }$

$\rm{\dashrightarrow 64 \times 12 = 4 \times 3}$

$\rm{\dashrightarrow \dfrac{\cancel{64} \times \cancel{12}}{ \cancel{4} \times \cancel{3}}}$

$\Large{\boxed{\bf{ \star \: 64 \: \star}}}$

❝ Hence, the no. discs to be made are 64 ❞

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