# Recent questions tagged geometry

1
A circular garden twenty feet in diameter is surrounded by a path three feet wide. What is the area of the path? $51 \pi$ square feet $60 \pi$ square feet $69 \pi$ square feet $90 \pi$ square feet
2
What is the area of a semicircle with a diameter of $16$ inches? $32 \pi$ square inches $64 \pi$ square inches $128 \pi$ square inches $256 \pi$ square inches
3
Which of the following figures has the largest perimeter $(1 \text{ foot} = 12 \text{ inches})$ a square with a diagonal of $5$ feet a rectangle with sides of $3$ feet and $4$ feet an equilateral triangle with a side equal to $48$ inches a regular hexagon whose longest diagonal is $6$ feet
4
The perimeter of a parallelogram is $50$ cm. The length of the parallelogram is $5$ cm more than the width. Find the length of the parallelogram. $15$ cm $11$ cm $5$ cm $10$ cm
5
A conical tent is to accommodate $10$ persons. Each person must have $6$ $m$^{2}$space to sit and$30m$^{2}$ of air to breath. What will be height of cone ? $37.5$ $m$ $150$ $m$ $75$ $m$ $15$ $m$
6
In a swimming-pool $90$ m by $40$ m, $150$ men take a dip. If the average displacement of water by a man is $8$ cubic metres, what will be rise in water level ? $30$ cm $33.33$ cm $20.33$ cm $25$ cm
7
If $A$ be the area of a right angled triangle and $b$ be one of the sides containing the right angle, then the length of altitude on the hypotenuse is : $\frac{2Ab}{\sqrt{4b^{4}+A^{2}}}$ $\frac{Ab}{\sqrt{b^{4}+4A^{2}}}$ $\frac{2Ab}{\sqrt{b^{4}+4A^{2}}}$ $\frac{Ab}{\sqrt{4b^{4}+A^{2}}}$
8
In an acute angled triangle $ABC$, if $\tan \left(A+B-C \right)=1$ and $\sec \left(B+C-A \right)=2$, Find angle $A$. $60^\circ$ $45^\circ$ $30^\circ$ $90^\circ$
9
What will be area of the rhombus with equations of sides $ax \pm$ $by \pm c$ = $1$ ? $\frac{3c^{2}}{ab}$sq. units $\frac{4c^{2}}{ab}$sq. units $\frac{2c^{2}}{ab}$sq. units $\frac{c^{2}}{ab}$sq. units
10
If $\left (-4, 0 \right), \left(1, -1 \right)$ are two vertices of a triangle whose area is $4$ Sq units then its third vertex lies on : $y=x$ $5x+y+12=0$ $x+5y-4=0$ $x-5y+4=0$
1 vote
11
In a triangle $XYZ$, $P$ and $Q$ are points on ${XY,XZ}$ respectively such that $XP=2PY$, $XQ=2QZ$, then the ratio, of area of $\triangle XPQ$ and area of $\triangle XYZ$ is: $4:9$ $2:3$ $3:2$ $9:4$
12
A conical tent is to accommodate $10$ persons. Each person must have $6m^{2}$ space to sit and $30m^{3}$ of air to breath. What will be height of cone? $37.5$ m $150$ m $75$ m $15$ m
13
In a bangle shop. If the shopkeeper displays the bangles in the form of a square then he is left with $38$ bangles. If he wanted to increase the size of square by one bangle each side of the square he found that $25$ bangles fall short of in completing the square. The actual number of bangles which he had with him the shop was_________. $1690$ $999$ $538$ $1000$
14
$A,B,C$ are three towns forming a triangle. A man has to walk from one town to next town, then ride to the next town then again drive towards his starting point. He can walk,ride,drive a km in $a,b,c$ minutes respectively. If he starts from $B$, he takes $a-b+c$ ... from $A$ he takes $c+b-a$ hrs. The length of the triangle is: (assume the motion in anticlockwise direction) $60a$ $50a$ $40a$ $65a$
15
A cylindrical box of radius $5$ cm contains $10$ solid spherical balls each of radius $5$ cm. If the topmost ball touches the upper cover of the box, then the volume of the empty space in the box is: $\dfrac{2500\pi}{3}$ cubic cm $500\pi$ cubic cm $2500\pi$ cubic cm $\dfrac{5000\pi}{3}$ cubic cm
16
If $(-4,0),(1,-1)$ are two vertices of a triangle whose area is $4$ Sq units then its third vertex lies on: $y=x$ $5x+y+12=0$ $x+5y-4=0$ $x-5y+4=0$
17
For a sphere of radius $10$ cm, the numerical value of the surface area is how many percent of the numerical value of its volume? $26.5\%$ $24\%$ $30\%$ $45\%$
18
Line $AB$ is $24$ metres in length and is tangent to the inner one of the two concentric circles at point $C.$ Points $A$ and $B$ lie on the circumference of the outer circle. It is known that the radii of the two circles are integers. The radius of the outer circle is $13$ m $5$ m $7$ m $4$ m
19
A rectangular field is to be fenced on three sides leaving a side of $20$ feet uncovered. If the area of the field is $680$ sq feet, how many feet of fencing will be required? $34$ $40$ $68$ $88$
20
If $10$, $12$ and '$x$' are sides of an acute angled triangle, how many integer values of '$x$' are possible ? $7$ $12$ $9$ $13$
21
The length of a rope, to which a cow is tied, is increased from $19$ m to $30$ m. How much additional ground will it be able to graze ? Assume that the cow is able to move on all sides with equal ease. Use $\pi = \frac{22}{7}$ in your calculations. $1696$ sq m $1694$ sq m $1594$ sq m $1756$ sq m
22
What is the measure of the radius of the circle that circumscribes a triangle whose sides measure $9, 40$ and $41$? $6$ $4$ $24.5$ $20.5$
23
A pole has to be erected on the boundary of a circular park of diameter $13$ meters in such a way that the difference of its distances from two diametrically opposite fixed gates $A$ and $B$ on the boundary is $7$ meters. The distance of the pole from one of the gates is: $8$ metres $8.25$ metres $5$ metres None these
24
From a square piece of card-board measuring $2a$ on each side of a box with no top is to be formed by cutting out from each corner a square with sides $b$ and bending up the flaps. The value of $b$ for which the box has the greatest volume is $b= \frac{a}{5}$ $b= \frac{a}{4}$ $b= \frac{2a}{3}$ $b= \frac{a}{2}$
1 vote
25
The sum of the areas of two circles which touch each other externally is $153\pi$. If the sum of their radii is $15$, find the ratio of the larger to the smaller radius $4$ $2$ $3$ None of these
26
$ABCD$ is a rectangle. The points $P$ and $Q$ lie on $AD$ and $AB$ respectively. If the triangle $PAQ, QBC$ and $PCD$ all have the same areas and $BQ = 2$, then $AQ =$ $1+\sqrt{5}$ $1-\sqrt{5}$ $\sqrt{7}$ $2\sqrt{7}$
1 vote
27
A car is approaching a light houise at uniform speed.The angle of elevation of car at the top of the light house changes from 45 to 60(IN DEGREES) in10 min.The time (in min) in which the car reach the base of the tower ?
28
a hollow iron pipe is 21cm long and its external diameter is 8cm. if the thickness of the pipe is 1 cm and iron weigth is 8 g/cm3 then the weigth of the pipe is?
29
Choose the best alternative: A right circular cone of height h’ is cut by a plane parallel to the base and at a distance h/3 from the vertex, then the volumes of the resulting cone and frustum are in the ratio: 1 : 3 8 : 19 1 : 4 1 : 7
30
Choose the best alternative A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of the cone and cylinder equal their diameters. Then their volumes are proportional, respectively to: 1:3:1 2:1:3 3:2:1 1:2:3
1 vote
31
What is the area of the triangle? I. Two sides are 41 cm each II. The altitude to the third side is 9 cm long. if the questions can be answered with the help of both the statements but not with the help of either statement itself. if the question can not be ... the question can be answered with the help $0$ statement $II$ alone if the question can be answered with the help of statement $I$ alone
32
What is the length of the rectangle ABCD? I. Area of the rectangle is 48 square units II. Length of the diagonal is 10 units If the questions can be answered with the help of both the statements but not with the help of either statement itself. If the question can ... can be answered with the help $0$ statement $II$ alone If the question can be answered with the help of statement $I$ alone
1 vote
33
The length of a ladder is exactly equal to the height of the wall it is resting against. If lower end of the ladder is kept on a stool of height $3$ m and the stool is kept $9$ m away from the wall, the upper end of the ladder coincides with the top of the wall. Then, the height of the wall is: $12$m $15$m $18$m $11$m
34
AB is the diameter of the circle and the points C and D are on the circumference such that $\angle CAD=30^o$. What is the measure of $\angle ACD$?
35
Choose the correct option: AB is perpendicular to BC and BD is perpendicular to AC. CE bisects the angle C; $\angle A=30^{\circ}$ Then, what is $\angle CED$? $30^{\circ}$ $60^{\circ}$ $45^{\circ}$ $65^{\circ}$
36
Choose the correct option: In the adjoining figure, $AC + AB = 5 AD$ and $AC – AD = 8$. The area of the rectangle ABCD is: $36$ $50$ $60$ Cannot be answered.
–1 vote
37
A closed wooden box of thickness $0.5$ cm and length $21$ cm, width $11$ cm, and height $6$ cm, is panted on the inside. The cost of painting is Rs $70$. What is the rate of painting in rupees per sq. cm? $0.7$ $0.5$ $0.1$ $0.2$
Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120$^o$. What is the ratio of the area of ABQCDP to the remaining area inside ABCD? ... $2 + \sqrt{3}$ $\frac{10-3 \sqrt{3} } {9}$ $1+ \frac{1}{\sqrt{3} }$ $2 \sqrt{3} -1$
In the given figure, $∠BAC = 120º$ and $AD$ is the bisector of $∠BAC$. If $\frac{(AD)(AB)}{BD} = \frac{AE}{EC}( AE + EC )$ and $∠EDC = ∠ECD$, what is the ratio of $∠B$ and $∠C$? 1 : 1 1 : 2 2 : 3 5 : 6