This question was previously asked in

UPSSSC Chakbandi Lekhpal Official Paper 1 (Held on : 30 Sept 2019 Shift 1)

Option 1 : 1232 cm^{3}

**Given:**

The radius of the base of a cone is 7 cm**.**

The slant height is 25 cm.

**Formula:**

Let the radius, height, slant height and volume of a cone be “r”, “h”, “l” and “v” respectively, Then

1) l^{2} = h^{2} + r^{2}

2) v = (1/3) × π × r^{2} × h

**Calculation:**

According to the question given,

The radius (r) and slant height (l) of a cone are 7 cm and 25 cm respectively.

According to the formula used,

25^{2} = h^{2} + 7^{2}

⇒ h^{2 }= 25^{2 }- 7^{2}

⇒ h^{2} = 625 – 49

⇒ h^{2} = 576

⇒ h = √576 = 24 cm.

The volume of the cone as per the formula:

(1/3) × π × 7^{2} × 24

⇒ (1/3) × (22/7) × 7^{2 }× 24

⇒ 22/3 × 7 × 24

⇒ 22 × 7 × 8

⇒ 1232 cm^{3}

**∴**** The volume of the cone is 1232 cm ^{3}.**