Change set

Pick exam & year, then Go.

Question map
Not attempted Correct Incorrect ★ Bookmarked
Loading…
Q4 (CISF/2019) Miscellaneous & General Knowledge › Important Days, Places & Events

A painter wants to paint a picture (rectangular portrait) occupying 72 square inches on a canvas allowing a margin of 4 inches on the top and at the bottom and 2 inches on each side. What will be the smallest dimension of the canvas?

Explanation

To find the smallest canvas area, let the dimensions of the rectangular picture be x (width) and y (height). The area of the picture is xy = 72 square inches.

The canvas dimensions include the margins: width W = x + 2 + 2 = x + 4, and height H = y + 4 + 4 = y + 8. The area of the canvas A is given by:

A = (x + 4)(y + 8)

Substituting y = 72/x into the equation:
A = (x + 4)(72/x + 8) = 72 + 8x + 288/x + 32 = 104 + 8x + 288/x

To minimize the area, we differentiate A with respect to x and set it to zero:
dA/dx = 8 - 288/x2 = 0 → x2 = 36 → x = 6 inches.

If x = 6, then y = 72/6 = 12. The canvas dimensions are (6 + 4) = 10" and (12 + 8) = 20". The area is 200 square inches, which is the smallest among the given options.

✓ Thank you! We'll review this.

SIMILAR QUESTIONS

CAPF · 2023 · Q21 Relevance score: -4.23

A rectangular wall is divided into four squares of equal size where there are two rows each having two squares. The top left square is colored with green. If, including green, there are three colors available and each square is colored using any one of these three colors such that no two adjacent squares get painted with the same color; then how many color combinations are possible?

IAS · 2000 · Q140 Relevance score: -5.46

A rectangular piece of iron sheet measuring 50 cm by 100 cm is rolled into a cylinder of height 50 cm. If the cost of painting the cylinder is Rs. 50 per square metre, then what will be the cost of painting the outer surface of the cylinder ?

NDA-II · 2009 · Q68 Relevance score: -6.14

An object is kept 5 cm in front of a concave mirror of focal length 15 cm. What will be the nature of the image?

IAS · 1996 · Q145 Relevance score: -6.39

The following figure contains three squares with areas of 100, 16 and 49 lying side by side as shown. By how much should the area of the middle square be reduced in order that the total length PQ of the resulting three squares is 19?