The cross-section of a 6 m long piece of metal is shown in the figure. Calculate :
(i) the area of the cross-section
(ii) the volume of the piece of metal in cubic centimeters.

Question

The cross-section of a 6 m long piece of metal is shown in the figure. Calculate : (i) the area of the cross-section (ii) the volume of the piece of metal in cubic centimeters.

KnowledgeBoat · Accepted Answer

From figure, AD = BC = 8 cm AB = CD = 6.5 cm Triangle sides = AE = 5 cm & DE = 5 cm Triangle base (AD) = 8 cm. Length of metal piece = 6 m = 600 cm. (i) Area of cross section : Calculating the area of rectangle ABCD, Area of rectangle ABCD = length × breadth = 8 × 6.5 = 52 cm2. EAD is an isosceles triangle, In an isosceles triangle, the perpendicular drawn from common vertex to the base, bisects the base. AF = FD = = 4 cm. By using pythagoras theorem for the triangle EFD, ⇒ Hypotenuse2 = Base2 + Height2 ⇒ ED2 = FD2 + EF2 ⇒ 52 = 42 + EF2 ⇒ 25 = 16 + EF2 ⇒ EF2 = 25 - 16 ⇒ EF2 = 9 ⇒ EF = ⇒ EF = 3 cm. ∴ Height (EF) = 3 cm Area of △ EAD = × Base × Height = × AD × EF = × 8 × 3 = 4 × 3 = 12 cm2. Total area = Area of rectangle ABCD + Area of triangle EAD = 52 + 12 = 64 cm2. Hence, area of cross-section = 64 cm2. (ii) Volume of metal: Volume of metal = Area of cross-section × Length of the metal piece = 64 × 600 = 38400 cm3. Hence, volume of metal = 38400 cm3.

Mathematics

The cross-section of a 6 m long piece of metal is shown in the figure. Calculate :
(i) the area of the cross-section
(ii) the volume of the piece of metal in cubic centimeters.

Mensuration

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Mathematics

The cross-section of a 6 m long piece of metal is shown in the figure. Calculate :(i) the area of the cross-section(ii) the volume of the piece of metal in cubic centimeters.

Mensuration

Related Questions

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(i) the area of its cross-section;
(ii) the volume of piece of metal;
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The adjoining figure shows the cross-section of a concrete wall to be constructed. It is 1.9 m wide at the bottom, 90 cm wide at the top and 5 m high. If its length is 20 m, find :
(i) the cross-sectional area;
(ii) the volume of the concrete in the wall.

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The area of cross-section of a rectangular pipe is 5.4 cm² and water is pumped out of it at the rate of 27 kmph. Find, in litres, the volume of water which flows out of the pipe in 1 minute.