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Q:

There is a cylinder circumscribing the hemisphere such that their bases are common. Find the ratio of their volumes

A) 3/2	B) 5/2
C) 7/2	D) 9/2

Answer & Explanation Answer: A) 3/2

Explanation:

R =OA = OB = Radius of hemisphere.
= Radius of cylinder ABCD.
Height of the cylinder = BC = radius

Volume of cylinder/Volume of hemisphere = $\frac{{πr}^{3}}{\frac{2}{3} {πr}^{3}}$

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Filed Under: Volume and Surface Area
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Q:

Mycolog is the branch of botany in which we study about

A) Algae	B) Fungi
C) Bacteria	D) Virus

Answer & Explanation Answer: B) Fungi

Explanation:

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Filed Under: Biology

Q:

Find the ratio of the surfaces of the inscribed and circumscribed spheres about a cube.

A) 1:2	B) 1;3
C) 1:4	D) 1:5

Answer & Explanation Answer: A) 1:2

Explanation:

$4 \times 3.14 \times r^{2} : 4 \times 3.14 \times {(\sqrt{r})}^{2} = 1 : 2$

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Filed Under: Volume and Surface Area
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Q:

Silviculture is the branch of botany in which we study about

A) Culture of algae	B) Development of forest
C) Culture of fungi	D) Silciphida plant

Answer & Explanation Answer: B) Development of forest

Explanation:

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Filed Under: Biology

Q:

A cylindrical rod of iron, whose height is equal to its radius, is melted and cast into spherical balls whose radius is half the radius of the rod. Find the number of balls.

A) 3	B) 4
C) 5	D) 6

Answer & Explanation Answer: D) 6

Explanation:

Volume of rod = ${πr}^{2} h$ = ${πr}^{2} \times r$ = ${πr}^{3}$

Volume of one spherical ball =r/2

Volume of the spherical ball = $\frac{\frac{4}{3} {πr}^{3}}{8}$

Number of balls=Volumeof rod/volumeof one ball

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Filed Under: Volume and Surface Area
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Q:

Branch of agriculture concerned with the production of crops

A) Agrotology	B) Agronomy
C) Agrostology	D) Anthropology

Answer & Explanation Answer: B) Agronomy

Explanation:

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Filed Under: Biology

Q:

Two cylindrical buckets have their diameters in the ratio 3:1 and their heights are as 1: 3. Find the ratio of their volumes.

A) 2:1	B) 3:1
C) 4:1	D) 5:1

Answer & Explanation Answer: B) 3:1

Explanation:

$\frac{v 1}{v 2} = \frac{{(r_{1})}^{2} \times h 1}{{(r_{2})}^{2} \times h 2}$

d1 = $2 r_{1}$ and d2 = $2 r_{2}$ are diameters

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Filed Under: Volume and Surface Area
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Q:

If the radius of base and height of a cone are increased by 10%, find the percentage of increase of its volume

A) 33.5%	B) 33.1%
C) 32.1%	D) 53.1%

Answer & Explanation Answer: B) 33.1%

Explanation:

v1= $\frac{1}{3} {πr}_{1}^{2} h_{1}$

v2= $\frac{1}{3} {πr}_{2}^{2} h_{2}$

% Increase in volume = (V2-V1) / (V2*100)

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Filed Under: Volume and Surface Area
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