Download App

Cylinder, Cone and Sphere — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsCylinder, Cone and Sphere4 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 $=\frac{7}{2} \times 2=7$
And length $=22-\frac{7}{2}=\frac{37}{2}=18.5\ m$
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 $=Rs. 4 \text{per} \ {m}^3$
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 "[4 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

Krithika wants to invest Rs 10,000 in shares of different companies such that the percentage return on her investment is 8%. She invested Rs 4,500 in 6% Rs 100 shares at Rs 75, Rs 2,500 in 8% Rs 100 shares at par and the rest in 16% Rs 100 shares. Find the rate at which she bought the 16% shares.
→
If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.
→
If $A=\left[\begin{array}{cc}3 & a \\ -4 & 8\end{array}\right], B=\left[\begin{array}{cc}c & 4 \\ -3 & 0\end{array}\right], C=\left[\begin{array}{cc}-1 & 4 \\ 3 & b\end{array}\right]$ and $3 A -2 C =6 B$, find the values of $a, b, c$.
→
A line through origin meets the line $x = 3y + 2$ at right angles at point $X$. Find the co-ordinates of $X$.
→
If $A =\left[\begin{array}{ll}1 & 3 \\ 3 & 4\end{array}\right] B =\left[\begin{array}{ll}-2 & 1 \\ -3 & 2\end{array}\right]$ and $A^2-5 B^2=5 C$ Find the matrix $C$ where $C$ is a $2$ by $2$ matrix.
→
If $\sin A+\cos A=m$ and $\sec A+\operatorname{cosec} A=n$, show that: $n\left(m^2-1\right)=2 m$
→
In a cyclic – quadrilateral PQRS, angle PQR = 135°. Sides SP and RQ produced meet at point A : whereas sides PQ and SR produced meet at point B.
If ∠A : ∠B = 2 : 1; find angles A and B.
→
If $x=\frac{2 a b}{a+b}$ find the value of $\frac{x+a}{x-a}+\frac{x+b}{x-b}$
→
If $\frac{a}{c}=\frac{c}{d}=\frac{c}{f}$ prove that:
$
\frac{a^2}{b^2}+\frac{c^2}{d^2}+\frac{e^2}{f^2}=\frac{ ac }{ bd }+\frac{ ce }{ df }+\frac{ ae }{ df }
$
→
In the given case below find
$(a)$ The order of matrix $M$.
$(b)$ The matrix $M$
$M \times\left[\begin{array}{ll}1 & 1 \\ 0 & 2\end{array}\right]=[1,2]$
→