Mathematics
A closed rectangular box is made of wood of 1.5 cm thickness. The exterior length and breadth are respectively 78 cm and 19 cm, and the capacity of the box is 15 cubic decimetres. Calculate the exterior height of the box.
Mensuration
26 Likes
Answer
Given:
External length of the box = 78 cm
External breadth of the box = 19 cm
Thickness of the wood = 1.5 cm
Volume of the box = 15 dm3 = 15,000 cm3
Let h be the external height of the box.
Volume of the box = l x b x h
⇒ (78 - (2 x 1.5) ) x (19 - (2 x 1.5) ) x (h - (2 x 1.5) ) cm3 = 15,000 cm3
⇒ (78 - 3) x (19 - 3) x (h - 3) cm3 = 15,000 cm3
⇒ 75 x 16 x (h - 3) cm3 = 15,000 cm3
⇒ 1,200 x (h - 3) cm3 = 15,000 cm3
⇒ (h - 3) = cm
⇒ h - 3 = 12.5 cm
⇒ h = 12.5 + 3 cm
⇒ h = 15.5 cm
Hence, the exterior height of the box is 15.5 cm.
Answered By
17 Likes
Related Questions
The external dimensions of a closed wooden box are 27 cm, 19 cm and 11 cm. If the thickness of the wood in the box is 1.5 cm; find :
(i) volume of the wood in the box;
(ii) the cost of the box, if wood costs ₹ 1.20 per cm3;
(iii) number of 4 cm cubes that could be placed into the box.
A tank 20 m long, 12 m wide and 8 m deep is to be made of iron sheet. It is open at the top. Determine the cost of iron-sheet, at the rate of ₹ 12.50 per metre, if the sheet is 2.5 m wide.
The square on the diagonal of a cube has an area of 1875 sq. cm. Calculate :
(i) the side of the cube.
(ii) the total surface area of the cube.
The following figure shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in centimetres. Assume that all angles in the figure are right angles.
