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ICSE Class 10 Mathematics Question 4 of 21

Solved 2024 Question Paper ICSE Class 10 Mathematics — Question 17

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17
Question

Question 2(ii)

A solid metallic cylinder is cut into two identical halves along its height. The diameter of the cylinder is 7 cm and the height is 10 cm. Find :

(a) The total surface area (both the halves).

(b) The total cost of painting the two halves at the rate of ₹ 30 per cm2.

(use π=227)\Big(\text{use } \pi = \dfrac{22}{7}\Big)

A solid metallic cylinder is cut into two identical halves along its height. The diameter of the cylinder is 7 cm and the height is 10 cm. Find : ICSE 2024 Maths Solved Question Paper.
Answer

(a) Given,

Diameter of cylinder (d) = 7 cm

Radius of cylinder (r) = d2=72\dfrac{d}{2} = \dfrac{7}{2} = 3.5 cm

Height of cylinder (h) = 10 cm

Total surface area (both the halves) = Total surface area of cylinder + Area of two rectangles

= [2πr(h + r)] + [2 × (l × b)]

= [2πr(h + r)] + [2 × (h × d)]

= [2×227×3.5×(3.5+10)]+[2×10×7]\Big[2 \times \dfrac{22}{7} \times 3.5 \times (3.5 + 10) \Big] + [2 \times 10 \times 7]

= (2 × 22 × 0.5 × 13.5) + 140

= 297 + 140

= 437 cm2.

Hence, total surface area of both the halves = 437 cm2.

(b) Total cost of painting the two halves = Total surface area × Rate

= 437 × 30

= ₹ 13,110.

Hence, total cost of painting the two halves = ₹ 13,110.