Question

Find the area of cross section, the lateral surface area, total surface area and the volume​

Answer 1

Hello Aryanstha372 !

Answer:

Assuming that the base of the Right Prism is an Equilateral Triangle,

Area of the Base = 25√3 cm²

Lateral Surface Area = 450 cm²

Total Surface Area = 50(9 + √3) cm²

Volume = 375√3 cm³

Step-by-step explanation:

Formulae :

LSA of a Right Prism = (Perimeter of the Base) × Height

TSA of a Right Prism = LSA + 2(Area of the Base)

Volume of a Right Prism = (Area of the Base) × Height

Given :

Assuming that the base of the Right Prism is equilateral,

a = 10 cm

Altitude of the triangular base = 8 cm

h = 15 cm

Procedure :

Assuming that the base is an equilateral triangle,

Area of the Base = $\frac{\sqrt{3} }{4} a^{2}$ units²

[Area of an equilateral triangle]

⇒ Area of the Base = $\frac{\sqrt{3} }{4} (10 \ cm)^{2}$

⇒ Area = $\frac{\sqrt{3} }{4} \times 100 \ cm^{2}$

⇒ Area = 25√3 cm².

LSA = p × h units²

⇒ LSA = (10 + 10 + 10) × 15

⇒ LSA = 30 × 15 cm²

∴ LSA  = 450 cm².

TSA = LSA + 2A

⇒ TSA = 450 cm² + 2(25√3 cm²)

⇒ TSA = 450 cm² + 50√3 cm²

⇒ TSA = 50(9 + √3) cm².

Volume = A × h

⇒ V = 25√3 cm² × 15 cm

⇒ V = 25 × 15 × √3 cm³

∴ Volume = 375√3 cm³.

Thanks !