The cross-section of a tunnel is a square of side 7 m surmounted by a semicircle as shown in the adjoining figure. The tunnel is 80 m long. Calculate:
(i) its volume,
(ii) the surface area of the tunnel (excluding the floor) and
(iii) its floor area.

Question

The cross-section of a tunnel is a square of side 7 m surmounted by a semicircle as shown in the adjoining figure. The tunnel is 80 m long. Calculate:
(i) its volume,
(ii) the surface area of the tunnel (excluding the floor) and
(iii) its floor area.

KnowledgeBoat · Accepted Answer

Given, Side of square (a) = 7 m Let radius of semi-circle be r metres. ⇒ 2r = 7 ⇒ r = m. Length of the tunnel (h) = 80 m Area of cross section of the front part = Area of square + Area of semi-circle = a² + = 7 x 7 + = 49 + = m². (i) By formula, Volume of the tunnel = Area of cross section x length of the tunnel = x 80 = 5460 m³. Hence, volume of tunnel = 5460 m³. (ii) Surface area of the tunnel (excluding the floor) = = Surface area of upper semi-circle portion + Surface area of square portion = πrh + ah + ah = = 880 + 560 + 560 = 2000 m². Hence, the surface area of the tunnel = 2000 m². (iii) Area of floor = Breadth x Length of tunnel = b x h = 80 x 7 = 560 m². Hence, area of floor = 560 m².

Mathematics

The cross-section of a tunnel is a square of side 7 m surmounted by a semicircle as shown in the adjoining figure. The tunnel is 80 m long. Calculate:
(i) its volume,
(ii) the surface area of the tunnel (excluding the floor) and
(iii) its floor area.

Mensuration

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Mathematics

The cross-section of a tunnel is a square of side 7 m surmounted by a semicircle as shown in the adjoining figure. The tunnel is 80 m long. Calculate:(i) its volume,(ii) the surface area of the tunnel (excluding the floor) and(iii) its floor area.

Mensuration

Related Questions

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Water flows, at 9 km per hour, through a cylindrical pipe of cross-sectional area 25 cm2. If this water is collected into a rectangular cistern of dimensions 7.5 m by 5 m by 4 m; calculate the rise in level in the cistern in 1 hour 15 minutes.

The cross-section of a tunnel is a square of side 7 m surmounted by a semicircle as shown in the adjoining figure. The tunnel is 80 m long. Calculate:
(i) its volume,
(ii) the surface area of the tunnel (excluding the floor) and
(iii) its floor area.

A cylindrical water tank of diameter 2.8 m and height 4.2 m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4 m s^-1. Calculate, in minutes, the time it takes to fill the tank.

Water flows, at 9 km per hour, through a cylindrical pipe of cross-sectional area 25 cm². If this water is collected into a rectangular cistern of dimensions 7.5 m by 5 m by 4 m; calculate the rise in level in the cistern in 1 hour 15 minutes.