Question

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A cap is shaped like the frustum of cone if its radius on the open side is 10 cm radius at the upper base is 4cm and its slant height is 15 cm find the area of material used for making it​

Answer 1

Step-by-step explanation:

Given:-

• A cap is in the shape of the frustum of a cone.

• The radius of the open side is 10cm.

• Radius of upper base is 4cm

• The slant height is 15cm.

To Find:-

• The area of the material used for making the cap.

Solution:-

Radius of open side (R) = 10cm

Radius of upper base (r) = 4cm

Slant height (l) = 15cm

Area of material used for making the cap = Curved surface area of frustum + Area of upper base.

Curved surface area of frustum = π(R + r) × l

Area if upper base ( circle) = πr²

Area of material

= (π(R + r) × l) + (πr²)

= $\bigg[\dfrac{22}{7} \times (10 + 4) \times 15 \bigg]+ \dfrac{22}{7} \times (4)^{2}$

= $\bigg[\dfrac{22}{7} \times 14 \times 15 \bigg]+ \dfrac{22}{7} \times 16$

= $\dfrac{22}{7} \big(14 \times 15 + 16\big)$

= $\dfrac{22}{7} \big(210 + 16\big)$

= $\dfrac{22}{7} \times 226$

= $\dfrac{4972}{7}$

= $710\dfrac{2}{7}$

∴ The Area of material used for making the cap is $710\dfrac{2}{7}cm^{2}$