Question

20) Find area of a trangle, sides of which are 8 cm, 11 cm and 13 cm
SECTION B 12 marks each)
21) Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m​

Answer 1

Solution!!

Let the sides be a, b and c, respectively.

a = 8 cm

b = 11 cm

c = 13 cm

We have to find the area of the triangle. So, we will use the Heron's formula.

Semi-perimeter (s) = (a + b + c)/2

s = (8 cm + 11 cm + 13 cm)/2

s = (32 cm)/2

s = 16 cm

Area = √[s(s-a)(s-b)(s-c)]

Area = √[16(16-8)(16-11)(16-13)]

Area = √[16(8)(5)(3)]

Area ≈ 43.82 cm²

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Diameter (d) = 24 cm

Radius (r) = d/2 = 24/2

r = 12 cm

Slant height (l) = 21 cm

We have to find the total surface area (TSA) of the cone.

TSA = πrl + πr²

TSA = [(22/7) × 12 cm × 21 cm] + [(22/7) × (12 cm)²]

TSA = [22 × 12 cm × 3 cm] + [(22/7) × 144 cm²]

TSA = [792 cm²] + [3168 cm²/7]

TSA = (5544 cm² + 3168 cm²)/7

TSA = (8712 cm²)/7

TSA ≈ 1244.58 cm²