Download App

Cylinder, Cone and Sphere — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsCylinder, Cone and Sphere3 Marks
Question
In the following diagram a rectangular platform with a semi-circular end on one side is $22$ metreslong from one end to the other end. If the length of the half circumference is $11$ metres. Find thecost of constructing the platform, $1.5$ metres high at the rate of Rs. $4$ per cubic metres.
✓

Answer

Length of the platform $= 22 m$
Circumference of semicircle $= 11 m$
$\therefore$ Radius $=\frac{c \times 2}{2 \times \pi}=\frac{11 \times 7}{22}=\frac{7}{2} m$
Therefore, breadth of the rectangular part $=\frac{7}{2} \times 2=7$
$\text { And length }=22-\frac{7}{2}=\frac{37}{2}=18.5 m$
$\text { Now area of platform }=1 \times b+\frac{1}{2} \pi r^2$
$=18.5 \times 7+\frac{1}{2} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} m ^2$
$=129.5+\frac{77}{4} m ^2$
$=148.75 m ^2$
Height of the platform $= 1.5 m$
$\therefore$ Volume $=148.75 \times 15=223.125 m ^3$
Rate of construction=Rs 4 perm ${ }^3$
Total expenditure=Rs $4 \times 223.125=$ Rs $892.50$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[3 marks sum]" from Cylinder, Cone and Sphere→Cylinder, Cone and Sphere — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

Draw a circle of radius 4 cm. Draw any diameter of the circle. At the end points of the diameter of the circle, draw tangents to the circle. Are they parallel?
→
The point P (5, -4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5. Find the co-ordinates of points A and B.
→
Prove the identity $(sin θ + cos θ) (tan θ + cot θ ) = sec θ + cosec θ$.
→
Two dice are rolled simultaneously, write down the total number of possible outcomes.
→
Solve each of the following equations using the formula:
$\frac{4}{x}-3=\frac{5}{2 x+3}$
→
The bisectors of ∠B and ∠C of a quadrilateral ABCD intersect each other at point P. Show that P is equidistant from the opposite sides AB and CD.
→
In the following two polynomials. Find the value of ‘a’ if $x + a$ is a factor of each of the two:
$x^3+ ax^2 - 2x + a + 4$
→
Find the area and perimeter of the following semi-circle :Diameter $= 7$cm
→
The radius of the internal and external surfaces of a hollow spherical shell are $3 cm$ and $5 cm$ respectively! If it is melted and recast into a solid cylinder of height $\frac{8}{3}$ cm, find the diameter of the cylinder.
→
From a solid right circular cylinder with height $10\ cm$ and radius of the base $6\ cm,$ a right circularcone of the same height and same base is removed. Find the volume of the remaining solid.
→