Surface Areas and Volumes Test

Result

Surface Areas and Volumes Test - 28

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

The volume of a frustum cone is 560 $$m^3$$, whose base and upper area of a circle is 90 and 10 $$m^2$$. Find the height of the cone.

A
40 cm

B
34 cm

C
24 cm

D
54 cm

Solution

Volume of a frustum cone = $$\frac{1}{3} (A_1 + A_2 + \sqrt{A_1 A_2 }) h$$
560 = $$\frac{1}{3} (90 + 10 + \sqrt{40 \times 10}) \times h$$
560 = $$\frac{1}{3} (50 + \sqrt{400}) \times h$$
560 = $$\frac{1}{3} (50+20) \times h$$
$$560 \times 3$$ = $$70 \times h$$
h = 1,680/70 = 24$$cm$$
Question 2
1 / -0

Calculate the volume of a frustum cone given below: (Use = 3.14)

A
640.8112 m$$^3$$

B
630.8112 m$$^3$$

C
620.8112 m$$^3$$

D
610.8112 m$$^3$$

Solution

Volume of the frustum cone is $$V = \displaystyle{\frac{\pi h}{3}}(R^2 + Rr + r^2)$$
R = 10 m, r = 0.2 m, h = 6 m
$$V = (3.14 \times 6)/(3)[10^2 + 10 \times 0.2 + 0.2^2]$$
$$= 3.14 x 2[100 + 2 + 0.04]$$
$$= 6.28[102.04]$$
$$= 640.8112\, m^3$$
Question 3
1 / -0

The base and top radius of a cone is 14 m and 8 m respectively. The height of the cone is 123 m. What is the volume of frustum of a cone? (Use $$\pi$$ = 3.14).

A
48,302.64 in

B
47,891.28 m

C
47,891.28 cm

D
47,891.28 m$$^3$$

Solution

Volume of the frustum cone V = $$\displaystyle{\frac{\pi h}{3}}(R^2 + Rr + r^2)$$
$$R = 14 m, r = 8 m, h = 123 m$$
$$V = (3.14 \times 123)/(3)[14^2 + 14 \times 8 + 8^2] $$
$$= 3.14 \times 41[196 + 112 + 64]$$
$$= 128.74[372]$$
$$= 47,891.28 m^3$$
Question 4
1 / -0

The base and top diameter of a cone is 0.5 m and 0.1 m respectively. The height of the cone is 12 m. What is the volume of frustum of a cone? (Use $$\pi$$ = 3).

A
12.88 m$$^3$$

B
13.88 m$$^3$$

C
15.88 m$$^3$$

D
14.88 m$$^3$$

Solution

Volume of the frustum cone is $$V = \displaystyle{\frac{\pi h}{3}}(R^2 + Rr + r^2)$$
D = 0.5 m, d = 0.1 m, h = 4 m
Diameter = radius/2
Radius = 2 $$\times$$ diameter
Therefore, R = 1 m, r = 0.2 m
$$V = (3 \times 12)/(3)[1^2 + 1 \times 0.2 + 0.2^2]$$
$$= 12[1 + 0.2 + 0.04]$$
$$=$$ 12[1.24]
$$=$$ 14.88 m$$^3$$
Question 5
1 / -0

Calculate the volume of a frustum cone given below: (Use $$\pi$$ = 3.14)

A
3,821.075 cm$$^3$$

B
3,921.075 cm$$^3$$

C
3,021.075 cm$$^3$$

D
3,121.075 cm$$^3$$

Solution

Volume of the frustum cone is $$V = \displaystyle{\frac{\pi h}{3}}(R^2 + Rr + r^2)$$
R = 15 cm, r = 1.5 cm, h = 15 cm
$$V = (3.14 \times 15)/(3)[15^2 + 15 \times 1.5 + 1.5^2]$$
$$= 3.14 \times 5[225 + 22.5 + 2.25]$$
$$= 15.7[249.75]$$
$$= 3,921.075 \,cm^3$$
Question 6
1 / -0

The volume of a frustum cone is $$210 \pi ft^3$$, whose base and upper area of a circle is 10 and 250 $$ft^2$$. Find the height of the cone. (Use $$\pi$$ = 22/7).

A
5.38 ft

B
4.38 ft

C
3.38 ft

D
6.38 ft

Solution

Volume of a frustum cone = $$\frac{1}{3} (A_1 + A_2 + \sqrt{A_1 A_2 }) h$$
$$210 \pi = \frac{1}{3} (10 + 250 + \sqrt{10 \times 250}) \times h$$
$$210 \pi = \frac{1}{3} (260 + \sqrt{2,500}) \times h$$
$$210 \pi = \frac{1}{3} (260+50) \times h$$
$$210 \times 22/7 \times 3 = 310 \times h$$
$$h = \frac{1,980}{310}$$
$$h =$$ 6.38 ft
Question 7
1 / -0

The base and top diameter of a cone is 12 cm and 2 cm respectively. The height of the cone is 360 cm. What is the volume of frustum of a cone? (Use $$\pi$$ = 3.14).

A
259,238.4 cm

B
259,238.4 m$$^3$$

C
259,238.4 cm$$^3$$

D
259,238.4 mm$$^3$$
Question 8
1 / -0

The surface area of the frustum cone is given its base radius, R = 12 cm and top radius, r = 10 cm. The height of the cone is 12 cm. Find the slant height of the cone.

A
$$2\sqrt{37}$$ cm

B
$$2\sqrt{5}$$ cm

C
24 cm

D
$$3\sqrt{5}$$ cm

Solution

Slant height of a cone = $$\sqrt{(R-r)^2 + h^2}$$
= $$\sqrt{(12-10)^2 + 12^2}$$
= $$\sqrt{(2)^2 + 144}$$
= $$\sqrt{148}$$
= $$2\sqrt{37}$$ cm
Question 9
1 / -0

Calculate the volume of a frustum cone given in figure: (Use $$\pi$$ = 3.14) where $$D$$ is diameter, $$r$$ is radius, $$h$$ is height.

A
3,7680 in$$^3$$

B
253,760 in$$^3$$

C
3,6680 in$$^3$$

D
12222 in$$^3$$

Solution

Volume of the frustum cone is $$V = \displaystyle{\frac{\pi h}{3}}(R^2 + Rr + r^2)$$
$$D = 20\ in, r = 10\ in, h = 120\ in$$
Diameter $$= 2$$ radius
$$R = 10\ in$$
$$V = (3.14 \times 120)/(3)[10^2 + 10 \times 10 + 10^2]$$
$$= 3.14 \times 40[100 + 100 + 100]$$
$$= 125.6[300]$$
$$= 3,7680\, in^3$$
Question 10
1 / -0

Calculate the volume of a frustum cone given below: (Use $$\pi$$ = 3.14)

A
113,829.168 in$$^3$$

B
103,829.168 in$$^3$$

C
123,829.168 in$$^3$$

D
133,829.168 in$$^3$$

Solution

Volume of the frustum cone is $$V = \displaystyle{\frac{\pi h}{3}}(R^2 + Rr + r^2)$$
D = 10 in, d = 2 in, h = 200 in
Diameter = radius/2
R = 20 in, r = 4 in
$$V = (3.14 \times 200)/(3)[20^2 + 20 \times 4 + 4^2]$$
$$= 209.333[400 + 80 + 16]$$
$$= 209.333[496]$$
$$= 103,829.168\, in^3$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 28

Result

Surface Areas and Volumes Test - 28

Score

-

Rank

-

SHARING IS CARING

Question 1

40 cm

34 cm

24 cm

54 cm

Solution

Question 2

640.8112 m$$^3$$

630.8112 m$$^3$$

620.8112 m$$^3$$

610.8112 m$$^3$$

Solution

Question 3

48,302.64 in

47,891.28 m

47,891.28 cm

47,891.28 m$$^3$$

Solution

Question 4

12.88 m$$^3$$

13.88 m$$^3$$

15.88 m$$^3$$

14.88 m$$^3$$

Solution

Question 5

3,821.075 cm$$^3$$

3,921.075 cm$$^3$$

3,021.075 cm$$^3$$

3,121.075 cm$$^3$$

Solution

Question 6

5.38 ft

4.38 ft

3.38 ft

6.38 ft

Solution

Question 7

259,238.4 cm

259,238.4 m$$^3$$

259,238.4 cm$$^3$$

259,238.4 mm$$^3$$

Question 8

$$2\sqrt{37}$$ cm

$$2\sqrt{5}$$ cm

24 cm

$$3\sqrt{5}$$ cm

Solution

Question 9

3,7680 in$$^3$$

253,760 in$$^3$$

3,6680 in$$^3$$

12222 in$$^3$$

Solution

Question 10

113,829.168 in$$^3$$

103,829.168 in$$^3$$

123,829.168 in$$^3$$

133,829.168 in$$^3$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.